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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2015-11-16</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000018926</issuerCik>
        <issuerName>CENTURYLINK, INC</issuerName>
        <issuerTradingSymbol>CTL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001659021</rptOwnerCik>
            <rptOwnerName>Landrieu Mary L.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CENTURYLINK, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>100 CENTURYLINK DRIVE</rptOwnerStreet2>
            <rptOwnerCity>MONROE</rptOwnerCity>
            <rptOwnerState>LA</rptOwnerState>
            <rptOwnerZipCode>71203</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Hope M. Spencer as Attorney-in-Fact for Mary L. Landrieu</signatureName>
        <signatureDate>2015-11-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
