<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>2117100 - Disclosure - Commitments and Contingencies</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001415020</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_CommitmentsAndContingenciesDisclosureAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Commitments and Contingencies Disclosure [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_CommitmentsAndContingenciesDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;Commitments and Contingencies&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Legal Matters&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Below are descriptions of certain legal actions that involve certain properties of TCM.&amp;#160;Although the results of legal actions cannot be predicted with certainty, it is the opinion of management that the resolution of these actions is not likely to have a material adverse effect on TCM's future consolidated financial position, results of operations or cash flows.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-align:left;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In May&amp;#160;2010, the Stellat'en First Nation filed a petition in the Supreme Court of British Columbia against the British Columbia Minister of Energy, Mines and Petroleum Resources and TCM alleging that the Endako Mine and the mill expansion project at the Endako Mine represent infringements of the aboriginal title of the petitioners and impacts to their aboriginal rights, and that the government breached its duty to consult with the Stellat'en First Nation in relation to the impacts of the Endako Mine and the mill expansion.&amp;#160;The petitioners sought a declaration that the Provincial Crown did not fulfill its duty to consult with them in relation to the mill expansion project, a declaration that the mining permits and/or tenures held by TCM are invalid, an order quashing or setting aside the decision to issue a permit amendment to TCM and an injunction prohibiting further construction or alterations relating to the mill expansion project. The matter was heard by the Supreme Court of British Columbia in a hearing that took place in the first quarter&amp;#160;of 2011.&amp;#160;In August 2011, the Court dismissed the petitioners' claims in full.&amp;#160;The Stellat'en First Nation subsequently filed a notice of appeal from that decision to the Court of Appeal of British Columbia seeking to have the decision of the Supreme Court of British Columbia set aside and seeking an order staying the permit amendment and any future permitting until the Province has engaged in further consultation. The government and TCM filed materials in response to the notice of appeal, and the matter was heard by the Court of Appeal in a hearing that took place in early November&amp;#160;2012. The timing of the release of the Court's decision in this matter is unknown.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-align:left;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In April 2012, the Stellat'en First Nation filed a new petition in the Supreme Court of British Columbia against the British Columbia Minister of Energy, Mine and Petroleum Resources and TCM making similar allegations to those discussed above in relation to a new permit amendment and new water license granted to TCM in March&amp;#160;2012 for the Endako Mine.&amp;#160;In April 2012, the parties agreed to put this matter into abeyance. No date for hearing the new petition has been set.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Molybdenum Purchases&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In the normal course of operations, TCM enters into agreements for the purchase of molybdenum. As of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, TCM had commitments to purchase approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;9.7 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; pounds of molybdenum sulfide concentrate throughout the remainder of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; to &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2016&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, to be priced at a discount to the market price for molybdenum oxide at the time of purchase.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Molybdenum Sales&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In the normal course of operations, TCM enters into certain molybdenum sales contracts where it sells future production at fixed prices. As of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, TCM had commitments to sell approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;300,000&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; pounds of molybdenum oxide for the remainder of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; through &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2015&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; at an average price of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$12.74&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; per pound.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Copper Concentrate Sales Agreements&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-align:left;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In 2012, TCM entered into &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;three&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; copper concentrate sales agreements, whereby TCM, among other things, agreed to sell an aggregate of approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;85%&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the copper-gold-silver concentrate produced at Mt. Milligan during 2013 and 2014 and an aggregate of approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;120,000&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; dry metric tons (&amp;#8220;DMT&amp;#8221;) in each of the two calendar years thereafter. Under one of the agreements, TCM has the option to sell to the counterparty, and the counterparty has the obligation to purchase from TCM, additional concentrate up to an amount equal to &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;40,000&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; DMT per year during each of 2015 and 2016. Pricing under these concentrate sales agreements will be determined by reference to specified published reference prices during the applicable quotation periods. Payment for the concentrate will be based on the price for the agreed copper, gold and silver content of the shipments delivered, less smelting and refining charges and certain other deductions, if applicable. The copper smelting and refining charges will be negotiated in good faith and agreed by the parties for each contract year based on terms generally acknowledged as industry benchmark terms. The gold and silver refining charges are as specified in the agreements.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Capital Purchase Commitments&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;As of June 30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, TCM had open purchase orders, contracts and capital purchase commitments of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$26.4 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for engineering and equipment related to the development of Mt. Milligan and open purchase orders, contracts and capital purchase commitments of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$26.2 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for the development of the permanent operations residence at Mt. Milligan.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Other Commitments and Contingencies&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In April 2010, TCM entered into a credit support agreement with British Columbia Hydro and Power Authority ("BC Hydro") related to the mill expansion project at the Endako Mine. Under this agreement, TCM is required to post financial assurance in an amount equal to BC Hydro's estimated out-of-pocket costs for work on the Endako mill expansion project. Subsequent to the commissioning of the new mill and subject to annual measurements of BC Hydro's incremental revenues following the mill's commissioning, some or all of this financial assurance may, thereafter, be released in amounts equal to the incremental revenues generated until such time as the full amount of financial assurance has been released or until such time as the expiration period has been reached. The amount of the financial assurance as of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; was approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;C$16.5 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;. The financial assurance is comprised of a guarantee for &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;C$5.3 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and a surety bond for approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;C$11.2 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;. Sojitz Moly Resources, Inc. (&amp;#8220;Sojitz&amp;#8221;) has agreed to reimburse TCM for &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;color:#000000;text-decoration:none;"&gt;25%&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of any amounts paid under the &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;C$5.3 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; guarantee. The surety bond can be drawn down in the event of a shortfall in incremental revenues after the commissioning of the new mill facility. At this time, TCM does not anticipate having to post any additional financial assurance with respect to the BC Hydro credit support agreement.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;As of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, a shortfall in Endako's future electric power usage that would result in incremental payments to BC Hydro cannot be determined and is not deemed to be probable. As such, no accrual has been recorded. An accrual for any expected shortfall will be recorded if and when it is determined that a shortfall is probable and a reasonable estimate can be made.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:10px;padding-top:10px;text-indent:32px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In October 2012, in contemplation of the deferral of Phase 8 stripping activities, TCM entered into arrangements with certain employees of the TC Mine designed to retain and reward eligible employees for their contribution to the continued successful operation of the TC Mine through the end of Phase 7. Employees who are eligible for participation in these arrangements are to be paid within &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;60&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; days of the end of Phase 7, as determined by the Company. Because of the uncertainty surrounding the number of employees who may remain through such date as well as when that date may be, it is not possible for management to estimate the likely amount to be paid under these arrangements. Currently, management estimates that TCM could be obligated to pay up to approximately &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$3.3 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; to such TC Mine employees under these arrangements.&lt;/font&gt;&lt;/div&gt;&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for commitments and contingencies.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.25)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 20

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6449706&amp;loc=d3e16207-108621



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 460

 -SubTopic 10

 -Section 50

 -Paragraph 8

 -URI http://asc.fasb.org/extlink&amp;oid=6398077&amp;loc=d3e12565-110249



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 450

 -SubTopic 20

 -Section 50

 -Paragraph 4

 -URI http://asc.fasb.org/extlink&amp;oid=25496072&amp;loc=d3e14435-108349



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 440

 -SubTopic 10

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=6394976&amp;loc=d3e25287-109308



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Commitments and Contingencies</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Commitments and Contingencies</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.thompsoncreekmetals.com/role/CommitmentsAndContingencies</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
