<?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>001170 - 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>FROM_Jan01_2013_TO_Jun30_2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000911421</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>Disclosure- Commitments and Contingencies [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="FROM_Jan01_2013_TO_Jun30_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p style='margin-top:9pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;margin-left:0px;"&gt;8&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;"&gt;. Commitments and Contingencies &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:4.5pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;font-style:italic;margin-left:0px;"&gt;(a) Concentration of Credit Risk &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:9pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-style:italic;margin-left:0px;"&gt;Financing receivables &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:4.5pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;Included in the Company's &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;Other&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; invested assets are certain notes receivable which meet the definition of financing receivables and are accounted for using the cost method of accounting. These notes receivable are collateralized by commercial or residential property. The Company utilizes a third party consultant to determine the initial investment criteria and to monitor the subsequent performance of the notes receivable. The process undertaken prior to the investment in these notes receivable includes an examination of the underlying collateral. The Company reviews its receivable positions on at least a quarterly basis using actual redemption experience. At June 30, 2013 and December 31, 2012&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, based on the latest available information, the Company recorded an allowance for credit losses related to these notes receivable of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;3.2&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million and $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;3.0 million&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, respectively. &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:9pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;The Company monitors the performance of the notes receivable based on the type of underlying collateral and by assigning a &amp;#8220;performing&amp;#8221; or a &amp;#8220;non-performing&amp;#8221; indicator of credit quality to each individual receivable. At June 30, 2013, the Company's notes receivable of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;44.0&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million were all performing and were collateralized by residential property and commercial property of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;30.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;1&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million and $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;13.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;9&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million, respectively. At December 31, 2012&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, the Company's notes receivable of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;46.7&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million were all performing and were collateralized by residential property and commercial property of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;31.3&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million and $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;15.4&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million, respectively.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:4.5pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;The Company purchased $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;27.0&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million and $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;27.2 million&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; of financing receivables during the &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;three months&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;and six months &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;ended June 30, 2013&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;The Company purchased $37.4 million of financing receivables during the three &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;months &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;and six months ended &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;June 30, 2012&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;. There wer&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;e no sales o&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;f financing receivables during the &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;three months&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;and six months &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;ended June 30, 2013 and 2012, however, the outstanding balances were reduced by settlements of the underlying debt. &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;font-style:italic;margin-left:0px;"&gt;(b) &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;font-style:italic;"&gt;Employment Agreements&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;In April 2013, the Company announced the restructuring of its business support operations into a single integrated worldwide support platform and changes to the structure of its Global Non-life Operations. The restructuring includes involuntary and voluntary employee termination plans in certain jurisdictions (collectively, termination plans). Employees affected by the termination plans have varying leaving date&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;s, largely through to mid-2014.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;During&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; the three months and six months ended &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;June 30, 2013&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, the Company recorded &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;a &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;pre-tax charge of $43.2 million related to the&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; costs of the&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; restructuring&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, which were primarily related to the termination plans, &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;within other operating expenses. &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;The continuing salary and other employment benefit costs related to the affected employees will be expensed as the employee &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;remains with the Company&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; and provides service&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;font-style:italic;margin-left:0px;"&gt;(c) &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;font-style:italic;"&gt;Legal Proceedings &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;There has been no significant change in legal proceedings at &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;June 30, 2013&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; compared to &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;December 31, 2012&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;. See Note 1&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;7&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;(e) to the Consolidated Financial Statements included in the Company's Annual Report on Form 10-K for the year ended December 31, 201&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;2&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;.&lt;/font&gt;&lt;/p&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 FASB Interpretation (FIN)

 -Number 14

 -Paragraph 3

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 2: 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 3: 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 4: 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 5: 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=6952336&amp;loc=d3e14435-108349



Reference 6: 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



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 5

 -Paragraph 9, 10, 11, 12

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



</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.partnerre.com/role/DisclosureCommitmentsAndContingencies</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
