<?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>0001795629</rptOwnerCik>
            <rptOwnerName>GEORGE AMY</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>Senior V.P. Human Resources</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2021-03-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.01</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>97444</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4737</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>401(k) plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </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 Ms. George's share ownership.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Scott J. Posner, by 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
0001795629
GEORGE AMY
C/O TEREX CORPORATION
45 GLOVER AVENUE
NORWALK
CT
06850
0
1
0
0
Senior V.P. Human Resources
Common Stock, $.01 par value
2021-03-24
4
F
0
1
47.01
D
97444
D
Common Stock, $.01 par value
4737
I
401(k) plan
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 Ms. George's share ownership.
/s/Scott J. Posner, by power of attorney
2021-03-26