<?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>1021 - Disclosure - Long-Term Debt</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>eol_PE798-----1310-Q0007_STD_181_20130630_0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000930236</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>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_LongTermDebtTextBlock</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="eol_PE798-----1310-Q0007_STD_181_20130630_0" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div&gt;
&lt;p style="MARGIN-TOP: 12pt; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt"&gt;
&lt;b&gt;Note 13. Long-Term Debt&lt;/b&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt"&gt;
&lt;i&gt;Commercial Borrowings&lt;/i&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; TEXT-INDENT: 4%; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt" align="justify"&gt;At June&amp;#xA0;30, 2013, we had one commercial loan
repurchase facility with an outstanding balance of $17 million and
a total borrowing limit of $150 million, with a remaining maturity
of 27 months. Borrowings under this facility are generally charged
interest based on a specified margin over the one-month LIBOR
interest rate. For the three and six months ended June&amp;#xA0;30,
2013, the average balance of this commercial borrowing was $17
million and $11 million, respectively. The fair value of commercial
loans pledged as collateral was $26 million at June&amp;#xA0;30, 2013.
The interest expense yield on this borrowing was 5.50% and 5.59%,
respectively, for the three and six months ended June&amp;#xA0;30,
2013. There was no balance on this warehouse facility at
December&amp;#xA0;31, 2012.&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; TEXT-INDENT: 4%; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt" align="justify"&gt;At June&amp;#xA0;30, 2013, we were in compliance with
all of the covenants related to our commercial loan repurchase
facility. Further information about the financial covenants under
this facility is set forth in Part I, Item&amp;#xA0;2 &amp;#x2013;
&lt;i&gt;Management&amp;#x2019;s Discussion and Analysis of Financial
Condition and Results of Operations&lt;/i&gt; of this Quarterly Report on
Form 10-Q.&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt"&gt;
Convertible Notes&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; TEXT-INDENT: 4%; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt" align="justify"&gt;In March 2013, we issued in a public offering
$287.5 million principal amount of 4.625% convertible senior notes
due 2018. These convertibles notes require semi-annual interest
distributions at a fixed coupon rate of 4.625% until maturity or
conversion, which will be no later than April&amp;#xA0;15, 2018. After
deducting the underwriting discount and offering costs, we received
approximately $279 million of net proceeds. Including amortization
of deferred securities issuance costs, the interest expense yield
on our convertibles notes was 5.53% and 5.48%, respectively, for
the three and six months ended June&amp;#xA0;30, 2013. At June&amp;#xA0;30,
2013, the accrued interest payable balance on this debt was $4
million.&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; TEXT-INDENT: 4%; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt" align="justify"&gt;Our convertible senior notes are convertible at the
option of the holder at a conversion rate of 41.1320 common shares
per $1,000 principal amount of convertible senior notes at
June&amp;#xA0;30, 2013 (equivalent to a conversion price of $24.31 per
common share). Upon conversion of these convertible senior notes by
a holder, the holder will receive shares our common stock.&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt"&gt;
&lt;i&gt;Trust Preferred Securities and Subordinated Notes&lt;/i&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; TEXT-INDENT: 4%; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt" align="justify"&gt;In 2006, we issued $100 million of trust preferred
securities through Redwood Capital Trust I, a Delaware statutory
trust, in a private placement transaction. These trust preferred
securities require quarterly distributions at a floating coupon
rate equal to three-month LIBOR plus 2.25% until the securities are
redeemed, which will be no later than January&amp;#xA0;30, 2037. The
interest expense yield on our trust preferred securities was 2.65%
and 2.91% for the six months ended June&amp;#xA0;30, 2013 and 2012,
respectively. Including hedging costs and amortization of deferred
securities issuance costs, the interest expense yield on our trust
preferred securities was 6.89% and 6.88% for the six months ended
June&amp;#xA0;30, 2013 and 2012, respectively. The earliest optional
redemption date without penalty was January&amp;#xA0;30, 2012. In
December 2010, we repurchased $500 thousand principal amount of
these trust preferred securities.&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; TEXT-INDENT: 4%; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt" align="justify"&gt;In 2007, we issued an additional $50 million of
subordinated notes. These subordinated notes require quarterly
distributions at a floating interest rate equal to six-month LIBOR
plus 2.25% until the notes are redeemed, which will be no later
than July&amp;#xA0;30, 2037. The interest expense yield on our
subordinated notes was 2.65% and 2.91% for the six months ended
June&amp;#xA0;30, 2013 and 2012, respectively. Including hedging costs
and amortization of deferred securities issuance costs, the
interest expense yield on our subordinated notes was 6.89% and
6.88% for the six months ended June&amp;#xA0;30, 2013 and 2012,
respectively. The earliest optional redemption date without a
penalty was July&amp;#xA0;30, 2012. In July 2009, we repurchased $10
million principal amount of this subordinated debt.&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12pt; TEXT-INDENT: 4%; FONT-FAMILY: Times New Roman; MARGIN-BOTTOM: 0pt; FONT-SIZE: 10pt" align="justify"&gt;At both June&amp;#xA0;30, 2013 and December&amp;#xA0;31,
2012, the accrued interest payable balance on this long-term debt
was less than $1 million. Under the terms of this long-term debt,
we covenant, among other things, to use our best efforts to
continue to qualify as a REIT. If an event of default were to occur
in respect of this long-term debt, we would generally be restricted
under its terms (subject to certain exceptions) from making
dividend distributions to stockholders, from repurchasing common
stock or repurchasing or redeeming any other then-outstanding
equity securities, and from making any other payments in respect of
any equity interests in us or in respect of any then-outstanding
debt that is &lt;i&gt;pari passu&lt;/i&gt; or subordinate to this long-term
debt.&lt;/p&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 long-term debt.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 22

 -Article 5



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.22)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Long-Term Debt</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Long-Term Debt</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.redwoodtrust.com/taxonomy/role/NotesToFinancialStatementsLongTermDebtTextBlock</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>1</NumberOfRows></InstanceReport>
