<?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>0001913836</rptOwnerCik>
            <rptOwnerName>Chow Gonzaga</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, Home Networks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>31781</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>12.20</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2020-08-09</value>
            </exerciseDate>
            <expirationDate>
                <value>2029-08-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>76900</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Performance Share Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-10-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>86770</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 12,110 restricted stock units that were granted on 06/01/2020 and will vest on 03/01/2023, subject to the reporting person's continued employment with the issuer.</footnote>
        <footnote id="F2">Includes 30,760 unvested options that will vest equally on 03/01/2023 and 03/01/2024, subject to the reporting person's continued employment with the issuer.</footnote>
        <footnote id="F3">Each performance share unit reflects the right to receive one share of common stock.  The performance share units vest upon the achievement of certain hurdles relating to the issuer's stock price ranging from a low of $17.50 to a high of $40, and the reporting person's continued employment with the issuer, over the period from 05/07/2021 to 10/01/2024.</footnote>
    </footnotes>

    <remarks></remarks>

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