<?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>2103100 - Disclosure - Discontinued Operations</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>D2013Q4YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000046640</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-04-30T00:00:00</PeriodStartDate><PeriodEndDate>2013-04-28T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="12 Months Ended" /><Label Key="Calendar" Id="1" Label="Apr. 28, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract</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>Discontinued Operations and Disposal Groups [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock</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="D2013Q4YTD" 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%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;Discontinued Operations &lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-left:48px;text-indent:-48px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:13px;text-align:justify;text-indent:12px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;In the third quarter of Fiscal 2013, the Company's Board of Directors approved management's plan to sell Shanghai LongFong Foods ("LongFong"), a maker of frozen products in China which was previously reported in the Asia/Pacific segment.  During the fourth quarter of Fiscal 2013, the Company secured an agreement with a buyer and expects the sale to close during the first quarter of Fiscal 2014.  As a result, LongFong's net assets were classified as held for sale and the Company adjusted the carrying value to estimated fair value, recording a &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$36.0 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; pre-tax and after-tax non-cash goodwill impairment charge to discontinued operations during the third quarter of Fiscal 2013.  The net assets held for sale related to LongFong as of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;April&amp;#160;28, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; are reported in Other current assets, Other non-current assets, Other accrued liabilities and Other non-current liabilities on the consolidated balance sheet as of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;April&amp;#160;28, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; as they are not material for separate balance sheet presentation.  &lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:13px;text-align:justify;text-indent:12px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;During the first quarter of Fiscal 2013, the Company completed the sale of its U.S. Foodservice frozen desserts business, resulting in a &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$32.7 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; pre-tax (&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$21.1 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; after-tax) loss which has been recorded in discontinued operations.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-bottom:13px;text-align:left;text-indent:12px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The operating results related to these businesses have been included in discontinued operations in the Company's consolidated statements of income for all periods presented.  The following table presents summarized operating results for these discontinued operations:&lt;/font&gt;&lt;div style="padding-left:0px;text-indent:0px;line-height:normal;padding-top:10px;"&gt;&lt;table cellpadding="0" cellspacing="0" style="font-family:Times New Roman;font-size:10pt;width:100%;border-collapse:collapse;text-align:left;"&gt;&lt;tr&gt;&lt;td colspan="4" rowspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td width="46%" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td width="18%" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td width="18%" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td width="18%" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:8pt;"&gt;&lt;font style="font-family:inherit;font-size:8pt;"&gt;&amp;#160;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan="3" style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1"&gt;&lt;div style="text-align:center;font-size:8pt;"&gt;&lt;font style="font-family:inherit;font-size:8pt;font-style:italic;"&gt;Fiscal Year Ended&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="overflow:hidden;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&amp;#160;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:8pt;"&gt;&lt;font style="font-family:inherit;font-size:8pt;font-style:italic;"&gt;April&amp;#160;28,&lt;br clear="none"/&gt;2013&lt;br clear="none"/&gt;FY 2013&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:8pt;"&gt;&lt;font style="font-family:inherit;font-size:8pt;font-style:italic;"&gt;April&amp;#160;29,&lt;br clear="none"/&gt;2012&lt;br clear="none"/&gt;FY 2012&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:8pt;"&gt;&lt;font style="font-family:inherit;font-size:8pt;font-style:italic;"&gt;April&amp;#160;27,&lt;br clear="none"/&gt;2011&lt;br clear="none"/&gt;FY 2011&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:8pt;"&gt;&lt;font style="font-family:inherit;font-size:8pt;"&gt;&amp;#160;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan="3" style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1"&gt;&lt;div style="text-align:center;font-size:8pt;"&gt;&lt;font style="font-family:inherit;font-size:8pt;font-style:italic;"&gt;(In millions)&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Sales&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$47.7&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$141.5&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$148.0&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Net after-tax losses&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$(17.6)&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$(51.2)&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$(39.6)&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Tax benefit on losses&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$0.6&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$1.4&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;background-color:#cceeff;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$2.6&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;/div&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 the facts and circumstances leading to the completed or expected disposal, manner and timing of disposal, the gain (loss) recognized in the income statement and the income statement caption that includes that gain (loss), amounts of revenues and pretax profit or loss reported in discontinued operations, the segment in which the disposal group was reported, and the classification (whether sold or classified as held for sale) and carrying value of the assets and liabilities comprising the disposal group. Includes all disposal groups, including those classified as components of the entity (discontinued operations).</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 144

 -Paragraph 43-48

 -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 360

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6391110&amp;loc=d3e2941-110230



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 20

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6360339&amp;loc=d3e1361-107760



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 20

 -Section 45

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6892542&amp;loc=d3e957-107759



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 20

 -Section 50

 -Paragraph 5

 -URI http://asc.fasb.org/extlink&amp;oid=6360339&amp;loc=d3e1510-107760



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 20

 -Section 45

 -Paragraph 4

 -URI http://asc.fasb.org/extlink&amp;oid=6892542&amp;loc=d3e1012-107759



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 20

 -Section 45

 -Paragraph 5

 -URI http://asc.fasb.org/extlink&amp;oid=6892542&amp;loc=d3e1020-107759



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 20

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6360339&amp;loc=d3e1474-107760



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 360

 -SubTopic 10

 -Section 45

 -Paragraph 5

 -URI http://asc.fasb.org/extlink&amp;oid=8077374&amp;loc=d3e2443-110228



Reference 10: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 205

 -SubTopic 20

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=6360339&amp;loc=d3e1436-107760



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Discontinued Operations</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Discontinued Operations</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.heinz.com/role/DiscontinuedOperations</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
