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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-03-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001406260</rptOwnerCik>
            <rptOwnerName>Clair Mark I</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>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>VP Controller &amp; CAO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2019-03-12</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4397</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>44852</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2019-03-12</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4083</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>48935</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2019-03-12</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4083</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>53018</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $.01 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>944</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 granted pursuant to one of the Company's long-term incentive plans with the award vesting as follows: 1/3 on March 12, 2020; 1/3 on March 12, 2021 and 1/3 on March 12, 2022.</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 2022 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, 2019 - December 31, 2021. 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 2022 if the Company achieves a targeted return on invested capital (&quot;ROIC&quot;) in each of 2019, 2020 and 2021. 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, by power of attorney</signatureName>
        <signatureDate>2019-03-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2019-03-12
0
0000097216
TEREX CORP
TEX
0001406260
Clair Mark I
TEREX CORPORATION
200 NYALA FARM ROAD
WESTPORT
CT
06880
0
1
0
0
VP Controller & CAO
Common Stock, $.01 par value
2019-03-12
4
A
0
4397
0
A
44852
D
Common Stock, $.01 par value
2019-03-12
4
A
0
4083
0
A
48935
D
Common Stock, $.01 par value
2019-03-12
4
A
0
4083
0
A
53018
D
Common Stock, $.01 par value
944
I
401(k) plan
Shares granted pursuant to one of the Company's long-term incentive plans with the award vesting as follows: 1/3 on March 12, 2020; 1/3 on March 12, 2021 and 1/3 on March 12, 2022.
Shares granted pursuant to one of the Company's long-term incentive plans with the award scheduled to vest in the first quarter of 2022 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, 2019 - December 31, 2021. 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 2022 if the Company achieves a targeted return on invested capital ("ROIC") in each of 2019, 2020 and 2021. 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, by power of attorney
2019-03-14