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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-08-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000917273</issuerCik>
        <issuerName>RAMBUS INC</issuerName>
        <issuerTradingSymbol>RMBS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001941085</rptOwnerCik>
            <rptOwnerName>Lynch Desmond</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O RAMBUS INC.</rptOwnerStreet1>
            <rptOwnerStreet2>4453 NORTH FIRST STREET, SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>SAN JOSE</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>95134</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34895</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reported shares are represented by 8,268 shares of RMBS stock, and restricted stock units, or RSUs, which vest as follows: (i) 9,000 RSUs vest in two equal installments beginning on March 2, 2023 or the first business day thereafter; (ii) 8,825 RSUs vest in three equal installments beginning on February 1, 2023 or the first business day thereafter; (iii) 8,802 RSUs vest in four equal annual installments beginning on February 1, 2023 or the first business day thereafter. Each RSU represents a contingent right to receive one share of RMBS common stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Brian Wu, by power of attorney</signatureName>
        <signatureDate>2022-08-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
