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

    <schemaVersion>X0303</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2010-12-31</periodOfReport>

    <form3HoldingsReported>0</form3HoldingsReported>

    <form4TransactionsReported>1</form4TransactionsReported>

    <issuer>
        <issuerCik>0000093751</issuerCik>
        <issuerName>STATE STREET Corp</issuerName>
        <issuerTradingSymbol>STT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001017402</rptOwnerCik>
            <rptOwnerName>WEISSMAN ROBERT E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O STATE STREET CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>ONE LINCOLN STREET</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02111</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>1990-05-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3728</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>73555</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">3,728 shares awarded to the reporting person on May 7, 1990 as director compensation, were inadvertently not reported at the time they were issued, and, consequently, were not reflected in subsquent Forms 4. The number of shares is reported on a post-split basis.</footnote>
        <footnote id="F2">Includes Director's stock compensation dividend equivalents acquired through December 31, 2010.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Shannon C. Stanley, Attorney-in-fact</signatureName>
        <signatureDate>2011-02-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
