<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>0204 - Disclosure - Acquisitions and Dispositions</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2011 - 4/1/2011
USD ($)

USD ($) / shares
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   &lt;!-- Begin Block Tagged Note 4 - lll:AcquisitionsAndDispositionsTextBlock--&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;table width="100%" border="0" cellpadding="0" cellspacing="0" style="font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent; text-align: left"&gt;
   &lt;tr&gt;
       &lt;td width="2%"&gt;&lt;/td&gt;
       &lt;td width="98%"&gt;&lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr valign="top"&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;4.&amp;#160;&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;Acquisitions
       and Dispositions&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;/table&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent"&gt;
       &lt;b&gt;&lt;i&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;2011
       Business Disposition&lt;/font&gt;&lt;/i&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 2%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       On February&amp;#160;22, 2011, the Company divested Microdyne
       Corporation (Microdyne), which was within the Electronic Systems
       segment. The divestiture resulted in an after-tax loss of
       approximately $1&amp;#160;million. Microdyne&amp;#8217;s annual revenues
       of approximately $8&amp;#160;million, operating results and net
       assets were not material for any period presented and,
       therefore, this divestiture is not reported as a discontinued
       operation.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent"&gt;
       &lt;b&gt;&lt;i&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;2010
       Business Acquisitions and Disposition&lt;/font&gt;&lt;/i&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 2%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       During the year ended December&amp;#160;31, 2010, in separate
       transactions, the Company acquired Insight Technology
       Incorporated (Insight), Airborne Technologies, Inc. (ATI), 3Di
       Technologies (3Di), and FUNA International GmbH (FUNA). In
       addition, the Company divested the InfraredVision Technology
       Corporation business. See Note&amp;#160;4 to the audited
       consolidated financial statements for the year ended
       December&amp;#160;31, 2010, included in the Company&amp;#8217;s Annual
       Report on
       &lt;font style="white-space: nowrap"&gt;Form&amp;#160;10-K&lt;/font&gt;
       for additional information regarding these business acquisitions
       and the disposition.
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak Begin --&gt;
   &lt;/div&gt;
   &lt;!-- END PAGE WIDTH --&gt;
   &lt;!-- PAGEBREAK --&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;!-- BEGIN PAGE WIDTH --&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent"&gt;
   &lt;b&gt;
   &lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;/font&gt;
   &lt;/b&gt;
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak End --&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 2%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       As of April&amp;#160;1, 2011, the purchase prices for Insight, ATI
       and 3Di were finalized and the Insight purchase price allocation
       was completed. The final purchase price for FUNA is subject to
       adjustment based on the closing date actual net assets. The
       final purchase price allocations for the ATI, 3Di, and FUNA
       business acquisitions are expected to be completed during the
       second quarter of 2011 and will be based on the final purchase
       prices and final appraisals and other analyses of fair values
       for acquired assets and assumed liabilities. The Company does
       not expect any of the differences between the preliminary and
       final purchase price allocations to have a material impact on
       its results of operations or financial position.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 2%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       &lt;b&gt;&lt;i&gt;Unaudited Pro Forma Statements of Operations Data&lt;/i&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 2%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       The following unaudited pro forma Statement of Operations data
       presents the combined results of the Company and its business
       acquisitions completed during the year ended December&amp;#160;31,
       2010, assuming that the business acquisitions completed during
       that period had occurred on January&amp;#160;1, 2010.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;table border="0" width="100%" align="center" cellpadding="0" cellspacing="0" style="font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent; text-align: left"&gt;
   &lt;!-- Table Width Row BEGIN --&gt;
   &lt;tr style="font-size: 1pt" valign="bottom"&gt;
       &lt;td width="75%"&gt;&amp;#160;&lt;/td&gt;&lt;!-- colindex=01 type=maindata --&gt;
       &lt;td width="10%"&gt;&amp;#160;&lt;/td&gt;&lt;!-- colindex=02 type=gutter --&gt;
       &lt;td width="7%" align="right"&gt;&amp;#160;&lt;/td&gt;&lt;!-- colindex=02 type=lead --&gt;
       &lt;td width="1%" align="right"&gt;&amp;#160;&lt;/td&gt;&lt;!-- colindex=02 type=body --&gt;
       &lt;td width="7%" align="left"&gt;&amp;#160;&lt;/td&gt;&lt;!-- colindex=02 type=hang1 --&gt;
   &lt;/tr&gt;
   &lt;!-- Table Width Row END --&gt;
   &lt;!-- TableOutputHead --&gt;
   &lt;tr style="font-size: 8pt" valign="bottom" align="center"&gt;
   &lt;td nowrap="nowrap" align="center" valign="bottom"&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td colspan="3" nowrap="nowrap" align="center" valign="bottom"&gt;
       &lt;b&gt;First Quarter Ended&lt;br /&gt;
       &lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr style="font-size: 8pt" valign="bottom" align="center"&gt;
   &lt;td nowrap="nowrap" align="center" valign="bottom"&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td colspan="3" nowrap="nowrap" align="center" valign="bottom" style="border-bottom: 1px solid #000000"&gt;
       &lt;b&gt;March&amp;#160;26, 2010&lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr style="font-size: 8pt" valign="bottom" align="center"&gt;
   &lt;td nowrap="nowrap" align="center" valign="bottom"&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td colspan="3" nowrap="nowrap" align="center" valign="bottom"&gt;
       &lt;b&gt;(in millions,&lt;br /&gt;
       &lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr style="font-size: 8pt" valign="bottom" align="center"&gt;
   &lt;td nowrap="nowrap" align="center" valign="bottom"&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td colspan="3" nowrap="nowrap" align="center" valign="bottom"&gt;
       &lt;b&gt;except per share data)&lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr style="line-height: 3pt; font-size: 1pt"&gt;
   &lt;td&gt;&amp;#160;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;!-- TableOutputBody --&gt;
   &lt;tr valign="bottom" style="background: #cceeff"&gt;
   &lt;td align="left" valign="bottom"&gt;
   &lt;div style="text-indent: -10pt; margin-left: 10pt"&gt;
       Pro forma net sales
   &lt;/div&gt;
   &lt;/td&gt;
   &lt;td&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="right" valign="bottom"&gt;
       $
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="right" valign="bottom"&gt;
       &amp;#160;&amp;#160;3,718
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="left" valign="bottom"&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr valign="bottom"&gt;
   &lt;td align="left" valign="bottom"&gt;
   &lt;div style="text-indent: -10pt; margin-left: 10pt"&gt;
       Pro forma net income attributable to L-3
   &lt;/div&gt;
   &lt;/td&gt;
   &lt;td&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="right" valign="bottom"&gt;
       $
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="right" valign="bottom"&gt;
       228
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="left" valign="bottom"&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr valign="bottom" style="background: #cceeff"&gt;
   &lt;td align="left" valign="bottom"&gt;
   &lt;div style="text-indent: -10pt; margin-left: 10pt"&gt;
       Pro forma diluted earnings per share
   &lt;/div&gt;
   &lt;/td&gt;
   &lt;td&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="right" valign="bottom"&gt;
       $
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="right" valign="bottom"&gt;
       1.93
   &lt;/td&gt;
   &lt;td nowrap="nowrap" align="left" valign="bottom"&gt;
   &amp;#160;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;/table&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 2%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       The unaudited pro forma results disclosed in the table above are
       based on various assumptions and are not necessarily indicative
       of the results of operations that would have occurred had the
       Company completed these acquisitions on January&amp;#160;1, 2010.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;/div&gt;
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