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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-02-23</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001656422</rptOwnerCik>
            <rptOwnerName>GARRISON JOHN L JR</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>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CHAIRMAN AND CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.01</value>
            </securityTitle>
            <transactionDate>
                <value>2021-02-23</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>17584</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.61</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>753552</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.01</value>
            </securityTitle>
            <transactionDate>
                <value>2021-02-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>32416</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>43.40</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>721136</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.01</value>
            </securityTitle>
            <transactionDate>
                <value>2021-02-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>79666</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>641470</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.01</value>
            </securityTitle>
            <transactionDate>
                <value>2021-02-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>30247</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>671717</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Transaction executed pursuant to a Rule 10b5-1 stock trading plan.</footnote>
        <footnote id="F2">Represents average sales price. Shares sold at various prices ranging from $42.50 to $42.89. Mr. Garrison will provide upon request by the SEC staff, Terex Corporation or a security holder of Terex Corporation, the full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F3">Represents average sales price. Shares sold at various prices ranging from $42.50 to $44.28. Mr. Garrison will provide upon request by the SEC staff, Terex Corporation or a security holder of Terex Corporation, the full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F4">Reflects shares of restricted stock forfeited by Mr. Garrison pursuant to the terms of performance awards granted in 2018, 2019 and 2020.</footnote>
        <footnote id="F5">Performance shares awarded pursuant to the terms of performance based awards granted in 2018, 2019 and 2020 resulting from the Company's exceeding performance targets set out in such grant for the period ended December 31, 2020.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Scott J. Posner, by power of attorney</signatureName>
        <signatureDate>2021-02-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2021-02-23
0
0000097216
TEREX CORP
TEX
0001656422
GARRISON JOHN L JR
C/O TEREX CORPORATION
45 GLOVER AVENUE
NORWALK
CT
06850
1
1
0
0
CHAIRMAN AND CEO
Common Stock, par value $.01
2021-02-23
4
S
0
17584
42.61
D
753552
D
Common Stock, par value $.01
2021-02-24
4
S
0
32416
43.40
D
721136
D
Common Stock, par value $.01
2021-02-24
4
D
0
79666
0
D
641470
D
Common Stock, par value $.01
2021-02-24
4
A
0
30247
0
A
671717
D
Transaction executed pursuant to a Rule 10b5-1 stock trading plan.
Represents average sales price. Shares sold at various prices ranging from $42.50 to $42.89. Mr. Garrison will provide upon request by the SEC staff, Terex Corporation or a security holder of Terex Corporation, the full information regarding the number of shares sold at each separate price.
Represents average sales price. Shares sold at various prices ranging from $42.50 to $44.28. Mr. Garrison will provide upon request by the SEC staff, Terex Corporation or a security holder of Terex Corporation, the full information regarding the number of shares sold at each separate price.
Reflects shares of restricted stock forfeited by Mr. Garrison pursuant to the terms of performance awards granted in 2018, 2019 and 2020.
Performance shares awarded pursuant to the terms of performance based awards granted in 2018, 2019 and 2020 resulting from the Company's exceeding performance targets set out in such grant for the period ended December 31, 2020.
/s/Scott J. Posner, by power of attorney
2021-02-25