<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-12-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001040161</issuerCik>
        <issuerName>PIXELWORKS, INC</issuerName>
        <issuerTradingSymbol>PXLW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001346543</rptOwnerCik>
            <rptOwnerName>Becker Drapkin Management, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 CRESCENT COURT</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1111</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of a  13(d) 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001451722</rptOwnerCik>
            <rptOwnerName>BECKER DRAPKIN PARTNERS (QP), L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 CRESCENT COURT, SUITE 1111</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of a 13(d) 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001451721</rptOwnerCik>
            <rptOwnerName>BECKER DRAPKIN PARTNERS, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 CRESCENT COURT, SUITE 1111</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of 13(d) 10% group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001349003</rptOwnerCik>
            <rptOwnerName>BC Advisors LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 CRESCENT COURT</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1111</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of a 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001537019</rptOwnerCik>
            <rptOwnerName>BD Partners IV, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 CRESCENT COURT</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1111</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of a 13(d) 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001349005</rptOwnerCik>
            <rptOwnerName>Becker Steven R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 CRESCENT COURT</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1111</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of a 13(d) 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001458693</rptOwnerCik>
            <rptOwnerName>Drapkin Matthew A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 CRESCENT COURT</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1111</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Member of a 13(d) 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>829700</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2011-12-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2524</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.3383</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1616216</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2011-12-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>376</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.3383</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>240269</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of common stock, par value $0.001 per share, of Pixelworks, Inc. (the &quot;Common Stock&quot;) directly beneficially owned by BD Partners IV, L.P. (&quot;BD Partners IV&quot;).</footnote>
        <footnote id="F2">Represents shares of Common Stock directly beneficially owned by Becker Drapkin Partners (QP), L.P. (&quot;Becker Drapkin QP&quot;).</footnote>
        <footnote id="F3">Represents shares of Common Stock directly beneficially owned by Becker Drapkin Partners, L.P. (&quot;Becker Drapkin, L.P.&quot;).</footnote>
        <footnote id="F4">Becker Drapkin Management, L.P. (&quot;BD Management&quot;), as the general partner of, and investment manager for, BD Partners IV, Becker Drapkin QP and Becker Drapkin, L.P. may be deemed to beneficially own the securities described in footnotes (1), (2) and (3).  BC Advisors, LLC (&quot;BCA&quot;), as the general partner of BD Management, and Steven R. Becker (&quot;Mr. Becker&quot;) and Matthew A. Drapkin (&quot;Mr. Drapkin&quot;), as the sole members and co-managing members of BCA and limited partners of BD Management, may in each case be deemed to be beneficial owners of the securities described in footnotes (1), (2) and (3).  In addition, each reporting owner may be deemed to beneficially own more than 10% of the Common Stock under Rule 16a-1(a)(1) under the Securities Exchange Act of 1934, as amended (the &quot;Exchange Act&quot;) as a result of being deemed a member of a group under Sections 13(d)(3) and 13(d)(5) of the Exchange Act.  (Continued in Footnote 5.)</footnote>
        <footnote id="F5">BD Management disclaims any beneficial ownership of all of the Common Stock listed herein, except to the extent of any pecuniary interest therein.  BD Partners IV disclaims beneficial ownership of the Common Stock described in footnotes (2) and (3). Becker Drapkin QP disclaims beneficial ownership of the Common Stock described in footnotes (1) and (3).  Becker Drapkin, L.P. disclaims beneficial ownership of the Common Stock described in footnotes (1) and (2).  BCA disclaims beneficial ownership of all of the Common Stock listed herein, except to the extent of any pecuniary interest therein.  Mr. Becker and Mr. Drapkin disclaim beneficial ownership of all of the Common Stock described herein, except to the extent of any pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>See Exhibit 99.1</signatureName>
        <signatureDate>2012-01-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
