<?xml version="1.0"?>
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    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-03-04</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>2021-03-04</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9811</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>183847</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.01</value>
            </securityTitle>
            <transactionDate>
                <value>2021-03-04</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9110</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>192957</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.01</value>
            </securityTitle>
            <transactionDate>
                <value>2021-03-04</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9110</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>202067</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Shares granted pursuant to one of the Company's long-term incentive plans with the award vesting as follows: 1/3 on March 4, 2022; 1/3 on March 4, 2023 and 1/3 on March 4, 2024.</footnote>
        <footnote id="F2">Shares granted pursuant to one of the Company's long-term incentive plans with the award scheduled to vest in the first quarter of 2024 if the Company achieves a targeted percentile rank against a peer group of companies for three year annualized total shareholder return (&quot;TSR&quot;) for the period January 1, 2021 - December 31, 2023. The number of shares in this grant are subject to adjustment, up or down, based upon attainment above or below the targeted percentile rank.</footnote>
        <footnote id="F3">Shares granted pursuant to one of the Company's long-term incentive plans with the award scheduled to vest in the first quarter of 2024 if the Company achieves a targeted return on invested capital (&quot;ROIC&quot;) in each of 2021, 2022 and 2023. The number of shares in this grant are subject to adjustment, up or down, based upon attainment above or below the targeted ROIC.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Scott J. Posner, power of attorney</signatureName>
        <signatureDate>2021-03-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2021-03-04
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
2021-03-04
4
A
0
9811
0
A
183847
D
Common Stock, par value $.01
2021-03-04
4
A
0
9110
0
A
192957
D
Common Stock, par value $.01
2021-03-04
4
A
0
9110
0
A
202067
D
Shares granted pursuant to one of the Company's long-term incentive plans with the award vesting as follows: 1/3 on March 4, 2022; 1/3 on March 4, 2023 and 1/3 on March 4, 2024.
Shares granted pursuant to one of the Company's long-term incentive plans with the award scheduled to vest in the first quarter of 2024 if the Company achieves a targeted percentile rank against a peer group of companies for three year annualized total shareholder return ("TSR") for the period January 1, 2021 - December 31, 2023. The number of shares in this grant are subject to adjustment, up or down, based upon attainment above or below the targeted percentile rank.
Shares granted pursuant to one of the Company's long-term incentive plans with the award scheduled to vest in the first quarter of 2024 if the Company achieves a targeted return on invested capital ("ROIC") in each of 2021, 2022 and 2023. The number of shares in this grant are subject to adjustment, up or down, based upon attainment above or below the targeted ROIC.
/s/Scott J. Posner, power of attorney
2021-03-08