<?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>009 - Disclosure - Acquisitions and Dispositions</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>1</Level><ElementName>us-gaap_BusinessCombinationsAbstract</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>Dispositions and Acquisitions [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_MergersAcquisitionsAndDispositionsDisclosuresTextBlock</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>verboseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Context_6ME__30-Jun-2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;
&lt;div align="justify" style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt; font-weight: bold;"&gt;&lt;font style="display: inline; text-decoration: underline;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt; font-weight: bold;"&gt;&lt;font style="display: inline; text-decoration: underline;"&gt;Note 3&amp;#8211; &lt;/font&gt;&lt;font style="display: inline; text-decoration: underline;"&gt;Acquisitions and &lt;/font&gt;&lt;font style="display: inline; text-decoration: underline;"&gt;Dispositions&lt;/font&gt;&lt;/font&gt;&lt;/font&gt;&lt;/font&gt;&lt;/div&gt;
&lt;div align="justify" style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&amp;#160;&lt;/div&gt;
&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;&lt;font style="display: inline; text-decoration: underline;"&gt;Liberty Participation Agreement&lt;/font&gt;&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;On September 17, 2012, Nytis LLC entered into a Participation Agreement (the &amp;#8220;Participation Agreement&amp;#8221;) with Liberty Energy LLC (&amp;#8220;Liberty&amp;#8221;), a Massachusetts limited liability company that allows Liberty to participate with Nytis LLC in the drilling and completion of wells on certain of Nytis LLC&amp;#8217;s leases located in Kentucky.&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&amp;#160;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;Pursuant to the Participation Agreement, Liberty paid Nytis LLC an initial payment of approximately $3.7 million in 2012.&amp;#160;&amp;#160;Upon receiving this initial payment, Nytis LLC assigned to Liberty a forty (40%) working interest in the covered leases.&amp;#160;&amp;#160;In addition to the initial payment, Liberty will carry a greater percentage of the costs associated with the first 20 wells drilled under the Participation Agreement subject to a maximum cap for any individual well, in addition to a maximum cap for the first 20 wells in the aggregate.&amp;#160;&amp;#160;Liberty committed to participate in the first 20 wells, of which 19 wells have been drilled as of June 30, 2013, on the basis described above. Following the drilling of the initial 20 wells, the parties will pay their respective costs on an unpromoted basis.&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;As the transaction did not significantly alter the relationship between capitalized costs and proved reserves, the Company did not recognize a gain or loss.&amp;#160;&amp;#160;The proceeds from the Participation Agreement were recorded as a reduction of the Company&amp;#8217;s investment in its oil and gas properties.&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;
&lt;div align="justify" style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt; font-weight: bold;"&gt;&lt;font style="display: inline; text-decoration: underline;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;&lt;font style="display: inline; font-weight: normal; text-decoration: underline;"&gt;Acquisitions&lt;/font&gt;&lt;/font&gt;&lt;/font&gt;&lt;/font&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;In May 2013, in two separate transactions, the Company acquired proved producing oil and gas properties and additional interests in partnerships with proved producing properties located in Kentucky and West Virginia for a total purchase price of approximately $517,000.&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&amp;#160;&lt;/div&gt;
&lt;div style="text-align: justify; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;
&lt;div align="justify" style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;The purchase of these assets qualified as a business combination and, as such, the Company estimated the fair value of the assets acquired and liabilities assumed as of the acquisition date (the date on which the Company obtained control of the properties.)&amp;#160;&amp;#160;The purchases of these assets were recorded as an investment in the Company&amp;#8217;s oil and gas properties.&amp;#160;&amp;#160;There is no significant difference between the fair value of the assets and the purchase price.&lt;/font&gt;&lt;/div&gt;
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