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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-02-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001795694</rptOwnerCik>
            <rptOwnerName>POSNER SCOTT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O TEREX CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>200 NYALA FARM ROAD</rptOwnerStreet2>
            <rptOwnerCity>WESTPORT</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06880</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior V.P., Gen Counsel Sec.</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9288</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>44068</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>8625</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>52693</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>8625</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>61318</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-27</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>536</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>60782</value>
                    <footnoteId id="F2"/>
                </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 February 26, 2021; 1/3 on February 26, 2022 and 1/3 on February 26, 2023.</footnote>
        <footnote id="F2">Ownership includes shares received as a dividend.</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 2023 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, 2020 - December 31, 2022. 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="F4">Shares granted pursuant to one of the Company's long-term incentive plans with the award scheduled to vest in the first quarter of 2023 if the Company achieves a targeted return on invested capital (&quot;ROIC&quot;) in each of 2020, 2021 and 2022. The number of shares in this grant are subject to adjustment, up or down, based upon attainment above or below the targeted ROIC.</footnote>
        <footnote id="F5">Reflects shares of restricted stock forfeited by Mr. Posner pursuant to the terms of performance awards granted in 2017, 2018 and 2019.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Scott J. Posner</signatureName>
        <signatureDate>2020-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_158292078199801.xml", "description": "FORM 4", "secsgml_size_bytes": 8937}]
X0306
4
2020-02-26
0
0000097216
TEREX CORP
TEX
0001795694
POSNER SCOTT
C/O TEREX CORPORATION
200 NYALA FARM ROAD
WESTPORT
CT
06880
0
1
0
0
Senior V.P., Gen Counsel Sec.
Common Stock, $.01 par value
2020-02-26
4
A
0
9288
0
A
44068
D
Common Stock, $.01 par value
2020-02-26
4
A
0
8625
0
A
52693
D
Common Stock, $.01 par value
2020-02-26
4
A
0
8625
0
A
61318
D
Common Stock, $.01 par value
2020-02-27
4
D
0
536
0
D
60782
D
Shares granted pursuant to one of the Company's long-term incentive plans with the award vesting as follows: 1/3 on February 26, 2021; 1/3 on February 26, 2022 and 1/3 on February 26, 2023.
Ownership includes shares received as a dividend.
Shares granted pursuant to one of the Company's long-term incentive plans with the award scheduled to vest in the first quarter of 2023 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, 2020 - December 31, 2022. 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 2023 if the Company achieves a targeted return on invested capital ("ROIC") in each of 2020, 2021 and 2022. The number of shares in this grant are subject to adjustment, up or down, based upon attainment above or below the targeted ROIC.
Reflects shares of restricted stock forfeited by Mr. Posner pursuant to the terms of performance awards granted in 2017, 2018 and 2019.
/s/Scott J. Posner
2020-02-28