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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-03-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000097216</issuerCik>
        <issuerName>TEREX CORP</issuerName>
        <issuerTradingSymbol>TEX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001488168</rptOwnerCik>
            <rptOwnerName>Hegarty Kieran</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O TEREX CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>45 GLOVER AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NORWALK</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06850</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President, Materials Processin</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.01</value>
            </securityTitle>
            <transactionDate>
                <value>2021-03-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.01</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>194304</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Shares are being withheld for payment of the tax liability associated with the vesting of previously granted restricted stock awards.</footnote>
        <footnote id="F2">Total share ownership as of March 24, 2021, reflects updated calculation of Mr. Hegarty's share ownership.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Scott J. Posner, power of attorney</signatureName>
        <signatureDate>2021-03-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2021-03-24
0
0000097216
TEREX CORP
TEX
0001488168
Hegarty Kieran
C/O TEREX CORPORATION
45 GLOVER AVENUE
NORWALK
CT
06850
0
1
0
0
President, Materials Processin
Common Stock, par value $.01
2021-03-24
4
F
0
4
47.01
D
194304
D
Shares are being withheld for payment of the tax liability associated with the vesting of previously granted restricted stock awards.
Total share ownership as of March 24, 2021, reflects updated calculation of Mr. Hegarty's share ownership.
/s/Scott J. Posner, power of attorney
2021-03-26