<?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>125 - Disclosure - Other Current Assets</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>4</Level><ElementName>opxa_OtherCurrentAssetsDisclosureTextBlock</ElementName><ElementPrefix>opxa_</ElementPrefix><IsBaseElement>false</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_PE10315---13S-1-0008_STD_90_20130331_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: 18px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;Note 3. Other Current
Assets&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 6px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Other current
assets consisted of the following at March&amp;#xA0;31, 2013 and
December&amp;#xA0;31, 2012:&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px; FONT-SIZE: 12px"&gt;
&amp;#xA0;&lt;/p&gt;
&lt;table style="BORDER-COLLAPSE: collapse" border="0" cellspacing="0" cellpadding="0" width="76%" align="center"&gt;
&lt;tr&gt;
&lt;td width="74%"&gt;&lt;/td&gt;
&lt;td valign="bottom" width="4%"&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td valign="bottom" width="4%"&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;
&lt;p style="BORDER-BOTTOM: #000000 1px solid; WIDTH: 39pt"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;b&gt;Description&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: #000000 1px solid" valign="bottom" colspan="2" align="center"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;b&gt;March&amp;#xA0;31,&lt;/b&gt;&lt;/font&gt;&lt;br /&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;b&gt;2013&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: #000000 1px solid" valign="bottom" colspan="2" align="center"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="1"&gt;&lt;b&gt;December&amp;#xA0;31,&lt;br /&gt;
2012&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Supplies
inventory&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;491,377&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;604,179&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Deferred offering
costs&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;309,969&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;341,166&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="TEXT-INDENT: -1em; MARGIN-LEFT: 1em"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Prepaid expenses&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;365,084&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;132,201&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="FONT-SIZE: 1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 1px solid"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;1,166,430&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;1,077,546&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" nowrap="nowrap"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="FONT-SIZE: 1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;
&lt;p style="BORDER-TOP: #000000 3px double"&gt;&amp;#xA0;&lt;/p&gt;
&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Supplies
inventory at March&amp;#xA0;31, 2013 and December&amp;#xA0;31, 2012
includes reagents and supplies that will be used to manufacture
Tcelna and placebo product in Opexa&amp;#x2019;s Phase IIb clinical
study. Opexa expects to amortize these prepaid reagents and
supplies to research and development costs in the consolidated
statements of expenses over the course of the clinical
study.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Deferred
offering costs at March&amp;#xA0;31, 2013 and December&amp;#xA0;31, 2012
include costs incurred from third parties in connection with the
implementation of an at-the-market program (&amp;#x201C;ATM
Agreement&amp;#x201D;) in September 2012 pursuant to which Opexa may
sell shares of its common stock from time to time depending upon
market demand through a sales agent in transactions deemed to be an
&amp;#x201C;at-the-market&amp;#x201D; offering as defined in Rule 415 of the
Securities Act of 1933. As of March&amp;#xA0;31, 2013, the remaining
costs of $88,446 in connection with the implementation of the ATM
Agreement remained capitalized and are included in other current
assets in the consolidated balance sheets. Upon the sales of shares
of common stock under the ATM Agreement, the remaining capitalized
costs are offset against the proceeds of such sales of shares of
common stock.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Deferred
offering costs at March&amp;#xA0;31, 2013 also include costs incurred
from third parties in connection with the implementation of a $1.5
million purchase agreement and a $15 million purchase agreement
(collectively, the &amp;#x201C;purchase agreements&amp;#x201D;) in November
2012 pursuant to which Opexa has the right to sell to Lincoln Park
Capital Fund, LLC (&amp;#x201C;Lincoln Park&amp;#x201D;) an aggregate of up
to $16.5 million in shares of its common stock, subject to certain
conditions and limitations. As of March&amp;#xA0;31, 2013, the
remaining costs of $221,523 in connection with the implementation
of the purchase agreements remained capitalized and are included in
other current assets in the consolidated balance sheets. Upon the
sales of shares of common stock under the purchase agreements, the
remaining capitalized costs are offset against the proceeds of such
sales of shares of common stock.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN-TOP: 12px; TEXT-INDENT: 4%; MARGIN-BOTTOM: 0px"&gt;
&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;Prepaid
expenses at March&amp;#xA0;31, 2013 include advance payments totaling
$220,374 made to vendors and consultants for the conduct of the
Phase IIb clinical trial in SPMS.&lt;/font&gt;&lt;/p&gt;
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