<?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>2115100 - Disclosure - Subsequent Events</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>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001330849</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_SubsequentEventsAbstract</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>Subsequent Events [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_SubsequentEventsTextBlock</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="D2013Q2YTD" 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%;padding-top:6px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;&amp;#160;Subsequent Events&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:6px;text-indent:30px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Subsequent to June 30, 2013, the Company noted the following:&lt;/font&gt;&lt;/div&gt;&lt;table cellpadding="0" cellspacing="0" style="padding-top:6px;font-family:Times New Roman; font-size:10pt;"&gt;&lt;tr&gt;&lt;td style="width:48px;" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:top" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;padding-left:30px;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&amp;#8226;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:top;" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;On &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;July&amp;#160;1, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company completed the sale of its fleet of Domestic Liftboats and related assets (see Note 5);&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;table cellpadding="0" cellspacing="0" style="padding-top:6px;font-family:Times New Roman; font-size:10pt;"&gt;&lt;tr&gt;&lt;td style="width:48px;" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:top" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;padding-left:30px;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&amp;#8226;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:top;" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;On &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;July&amp;#160;5, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company completed the purchase of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;6.2 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; shares of Discovery common stock at &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;15&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; NOK (USD &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$15.2 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;), increasing its total interest in Discovery to &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;96%&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;table cellpadding="0" cellspacing="0" style="padding-top:6px;font-family:Times New Roman; font-size:10pt;"&gt;&lt;tr&gt;&lt;td style="width:48px;" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:top" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;padding-left:30px;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&amp;#8226;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:top;" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;On &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;July&amp;#160;8, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company issued &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$400.0 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; aggregate principal amount of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;8.75%&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; Senior Notes due 2021 and amended its Credit Agreement (See Note 6);&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;table cellpadding="0" cellspacing="0" style="padding-top:6px;font-family:Times New Roman; font-size:10pt;"&gt;&lt;tr&gt;&lt;td style="width:48px;" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:top" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;padding-left:30px;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&amp;#8226;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:top;" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;On &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;July&amp;#160;22, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company closed on the sale of the Inland assets (See Note 5);&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;table cellpadding="0" cellspacing="0" style="padding-top:6px;font-family:Times New Roman; font-size:10pt;"&gt;&lt;tr&gt;&lt;td style="width:48px;" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:top" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;padding-left:30px;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&amp;#8226;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:top;" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;On &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;July&amp;#160;23, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, Discovery paid &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$166.9 million&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; for the final shipyard installment on &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Discovery Triumph&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;; and&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;table cellpadding="0" cellspacing="0" style="padding-top:6px;font-family:Times New Roman; font-size:10pt;"&gt;&lt;tr&gt;&lt;td style="width:48px;" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:top" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;padding-left:30px;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&amp;#8226;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:top;" rowspan="1" colspan="1"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;On &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;July&amp;#160;23, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company's jackup drilling rig &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;font-style:italic;"&gt;Hercules 265 &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;experienced a well control incident (See Note 12).&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&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 significant events or transactions that occurred after the balance sheet date through the date the financial statements were issued or the date the financial statements were available to be issued. 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