<?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>107 - Disclosure - Related Party Transactions</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>from-2013-01-01-to-2013-06-30.771.0.0.0.0.0.0.0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001037049</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_RelatedPartyTransactionsAbstract</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>Related Party Transactions [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_RelatedPartyTransactionsDisclosureTextBlock</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="from-2013-01-01-to-2013-06-30.771.0.0.0.0.0.0.0" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;&lt;div&gt; &lt;div&gt;&lt;!--StartFragment--&gt; &lt;table style="MARGIN-BOTTOM: 0pt; FONT: bold 10pt Times New Roman, Times, Serif; MARGIN-TOP: 0pt" cellspacing="0" cellpadding="0" width="100%"&gt; &lt;tr style="VERTICAL-ALIGN: top"&gt; &lt;td style="WIDTH: 0px"&gt;&amp;nbsp;&lt;/td&gt; &lt;td style="WIDTH: 0.5in"&gt;7.&lt;/td&gt; &lt;td style="TEXT-ALIGN: justify"&gt;Related Party Transactions&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px"&gt; &amp;nbsp;&lt;/p&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px"&gt; Related party transactions not disclosed elsewhere in these interim consolidated financial statements include:&lt;/p&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px 0pt 0.5in; BACKGROUND-COLOR: white; TEXT-INDENT: -0.25in"&gt; &amp;nbsp;&lt;/p&gt; &lt;table style="MARGIN-BOTTOM: 0pt; FONT: 10pt Times New Roman, Times, Serif; MARGIN-TOP: 0pt; BACKGROUND-COLOR: white" cellspacing="0" cellpadding="0" width="100%"&gt; &lt;tr style="VERTICAL-ALIGN: top"&gt; &lt;td style="WIDTH: 0.25in"&gt;&amp;nbsp;&lt;/td&gt; &lt;td style="WIDTH: 0.25in"&gt;a)&lt;/td&gt; &lt;td style="TEXT-ALIGN: justify"&gt;During the six months ended June 30, 2013 consulting fees of $317,000 (June 30, 2012: $202,023) were incurred to directors and officers (or companies of the officers and directors) of the Company. The transactions were recorded at the exchange amount, being the value established and agreed to by the related parties.&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p style="FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px 0pt 0.5in; BACKGROUND-COLOR: white; TEXT-INDENT: -0.25in"&gt; &amp;nbsp;&lt;/p&gt; &lt;table style="MARGIN-BOTTOM: 0pt; FONT: 10pt Times New Roman, Times, Serif; MARGIN-TOP: 0pt; BACKGROUND-COLOR: white" cellspacing="0" cellpadding="0" width="100%"&gt; &lt;tr style="VERTICAL-ALIGN: top"&gt; &lt;td style="WIDTH: 0.25in"&gt;&amp;nbsp;&lt;/td&gt; &lt;td style="WIDTH: 0.25in"&gt;b)&lt;/td&gt; &lt;td&gt;Coresco (a company that the CEO and CFO are affiliated with) also charged for geophysical consulting activities and other exploration management fees for a total of $63,000 during the six months ended June 30, 2013 (June 30, 2012: $nil)&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px 0pt 0.5in; BACKGROUND-COLOR: white; TEXT-INDENT: -0.25in"&gt; &amp;nbsp;&lt;/p&gt; &lt;table style="MARGIN-BOTTOM: 0pt; FONT: 10pt Times New Roman, Times, Serif; MARGIN-TOP: 0pt; BACKGROUND-COLOR: white" cellspacing="0" cellpadding="0" width="100%"&gt; &lt;tr style="VERTICAL-ALIGN: top"&gt; &lt;td style="WIDTH: 0.25in"&gt;&amp;nbsp;&lt;/td&gt; &lt;td style="WIDTH: 0.25in"&gt;c)&lt;/td&gt; &lt;td style="TEXT-ALIGN: justify"&gt;Included in accounts payable and accrued expenses and advances payable (related parties) as at June 30, 2013 and December 31, 2012 were $148,049 and $158,220 respectively payable to officers and directors of the Company for consulting fees and various expenses incurred on behalf of the Company.&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;!--EndFragment--&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 related party transactions. Examples of related party transactions include transactions between (a) a parent company and its subsidiary; (b) subsidiaries of a common parent; (c) and entity and its principal owners; and (d) affiliates.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 4

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39622-107864



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39603-107864



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39549-107864



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

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 04

 -Paragraph b

 -Article 3A



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 235

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.4-08.(k))

 -URI http://asc.fasb.org/extlink&amp;oid=26873400&amp;loc=d3e23780-122690



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

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 08

 -Paragraph k

 -Article 4



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 6

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39691-107864



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 850

 -SubTopic 10

 -Section 50

 -Paragraph 5

 -URI http://asc.fasb.org/extlink&amp;oid=6457730&amp;loc=d3e39678-107864



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Related Party Transactions</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Related Party Transactions</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://aurora-gold.com/role/RelatedPartyTransactions</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
