<?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>1170 - Disclosure - Subsequent Events</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>1/1/2010 - 12/31/2010
USD ($)
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>D2010</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000047129</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2010-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2010-12-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="12 Months Ended" /><Label Id="2" Label="Dec. 31, 2010" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>hzc_SubsequentEventsDisclosureAbstract</ElementName><ElementPrefix>hzc</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>No definition available.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Subsequent Events</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_ScheduleOfSubsequentEventsTextBlock</ElementName><ElementPrefix>us-gaap</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;table style="font-size:10pt; font-family:'Times New Roman',times,serif;"&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="FONT-FAMILY: arial; TEXT-ALIGN: justify"&gt;&lt;font size="2"&gt;&lt;b&gt;Note&amp;nbsp;17&amp;#151;Subsequent Events &lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="FONT-FAMILY: arial; TEXT-ALIGN: justify"&gt;&lt;font size="2"&gt;In January 2011, Gerald A. Plescia, President, Hertz Equipment Rental Corporation, or "HERC," retired from the Company. Mark P. Frissora, our Chairman and Chief Executive Officer is assuming the temporary senior management responsibility for HERC until a successor is named. &lt;/font&gt;&lt;/p&gt;
&lt;p style="FONT-FAMILY: arial; TEXT-ALIGN: justify"&gt;&lt;font size="2"&gt;In January 2011, Hertz redeemed in full its outstanding ($518.5&amp;nbsp;million principal amount) 10.5% Senior Subordinated Notes due 2016 which resulted in premiums paid of $27.2&amp;nbsp;million and the write-off of unamortized debt costs of $8.6&amp;nbsp;million. In January and February 2011, Hertz redeemed $1,105&amp;nbsp;million principal amount of its outstanding 8.875% Senior Notes due 2014 which resulted in premiums paid of $24.5&amp;nbsp;million and the write-off of unamortized debt costs of $14.4&amp;nbsp;million. We used the proceeds from the September 2010 issuance of $700&amp;nbsp;million aggregate principal amount of 7.50% Senior Notes, the December 2010 issuance of $500&amp;nbsp;million aggregate principal amount of 7.375% Senior Notes and the February 2011 issuance of $500&amp;nbsp;million aggregate principal amount of 6.75% Senior Notes (see below) for these redemptions. &lt;/font&gt;&lt;/p&gt;
&lt;p style="FONT-FAMILY: arial; TEXT-ALIGN: justify"&gt;&lt;font size="2"&gt;In February 2011, Hertz issued $500&amp;nbsp;million aggregate principal amount of 6.75% Senior Notes due 2019. The 6.75% Senior Notes are guaranteed on a senior unsecured basis by the domestic subsidiaries of Hertz that guarantee its Senior Credit Facilities. &lt;/font&gt;&lt;/p&gt;
&lt;p style="FONT-FAMILY: arial; TEXT-ALIGN: justify"&gt;&lt;font size="2"&gt;In February 2011, Hertz used existing corporate liquidity to pay off the maturing amount of the Brazilian Fleet Financing Facility. &lt;/font&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;
</NonNumbericText><NonNumericTextHeader>Note&amp;nbsp;17&amp;#151;Subsequent Events
In January 2011, Gerald A. Plescia, President, Hertz Equipment Rental Corporation, or "HERC," retired from the Company.</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>Describes disclosed significant events or transactions that occurred after the balance sheet date, but before the issuance of the financial statements. Examples include: the sale of a capital stock issue, purchase of a business, settlement of litigation, losses resulting from fire or flood, losses on receivables, significant realized and unrealized gains and losses that result from changes in quoted market prices of securities, declines in market prices of inventory, changes in authorized or issued debt (SEC), significant foreign exchange rate changes, substantial loans to insiders or affiliates, significant long-term investments, and substantial dividends not in the ordinary course of business.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 5
 -Paragraph 11

</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Subsequent Events</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>Subsequent Events</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
