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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-03-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001517228</issuerCik>
        <issuerName>CommScope Holding Company, Inc.</issuerName>
        <issuerTradingSymbol>COMM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001913770</rptOwnerCik>
            <rptOwnerName>Sucharczuk Guy</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O COMMSCOPE HOLDING COMPANY, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>1100 COMMSCOPE PLACE SE</rptOwnerStreet2>
            <rptOwnerCity>HICKORY</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP &amp; President, ANS</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>105644</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Includes (a) 2,591 restricted stock units that were granted on 04/04/2019 and will vest on 03/30/2022; (b) 10,597 restricted stock units that were granted on 06/01/2020 and will vest on 03/01/2023; (c) 19,379 restricted stock units that were granted on 06/01/2021 and will vest ratably on 06/01/2022, 06/01/2023 and 06/01/2024; and (d) 50,000 restricted stock units that were granted on 03/01/2022 and will vest ratably on 06/01/2023, 06/01/2024 and 06/01/2025, each subject to the reporting person's continued employment with the issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Michael D. Coppin, under a Power of Attorney</signatureName>
        <signatureDate>2022-03-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
