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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2013-03-14</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001498828</issuerCik>
        <issuerName>Howard Hughes Corp</issuerName>
        <issuerTradingSymbol>HHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001167987</rptOwnerCik>
            <rptOwnerName>LAYNE PAUL H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE GALLERIA TOWER,</rptOwnerStreet1>
            <rptOwnerStreet2>13355 NOEL ROAD, 22ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75240</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Master Plan. Com.</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14900</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>NQ Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>67.11</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2017-04-30</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2022-04-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>50000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock granted pursuant to The Howard Hughes Corporation 2010 Amended and Restated Incentive Plan.  The shares vest on April 30, 2017, unless earlier vested in accordance with the terms of the restricted stock agreement, dated as of Apil 30, 2012, by and between The Howard Hughes Corporation and Paul H. Layne.</footnote>
        <footnote id="F2">These options were granted on April 30, 2012 and become exercisable after April 30, 2017.  Upon death or Permanent Disability (as defined in the award agreement), the options will be deemed to vest at a rate of 20% per year and the vested options will be immediately exercisable. Any or all of the options may become immediately exercisable upon retirement in the sole discretion of the Chief Executive Officer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Timothy F. Hubach,
Attorney-in-fact for
Paul H. Layne</signatureName>
        <signatureDate>2013-03-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
