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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2015-03-10</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000045876</issuerCik>
        <issuerName>HARSCO CORP</issuerName>
        <issuerTradingSymbol>HSC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001636757</rptOwnerCik>
            <rptOwnerName>Hochman Russell C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>350 POPLAR CHURCH ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CAMP HILL</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>17011</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>false</isDirector>
            <isOfficer>true</isOfficer>
            <isTenPercentOwner>false</isTenPercentOwner>
            <isOther>false</isOther>
            <officerTitle>VP &amp;amp; Interim Gen. Counsel</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Appreciation Rights</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>25.93</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2015-05-09</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-05-09</value>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>HSC Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7258</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>HSC Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1404</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>HSC Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2285</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2285</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The stock appreciation rights vest in annual 33 1/3% increments on each of the first three anniversaries of the date of grant.</footnote>
        <footnote id="F2">Restricted stock units granted under the 2013 Equity and Incentive Compensation Plan represent a contingent right to receive Harsco common stock on a one-for-one basis when the restricted stock units vest.  Each restricted stock unit vests on the third anniversary of the grant date.</footnote>
        <footnote id="F3">Each performance share unit represents a contingent right to receive the equivalent of one share of Harsco common stock.  The performance share units vest based on the total shareholder return of Harsco common stock relative to the S&amp;P MidCap 400 Industrial Index. The performance share units vest on 12/31/2016.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Russell C. Hochman</signatureName>
        <signatureDate>2015-03-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
