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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-10-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001674416</issuerCik>
        <issuerName>CRISPR Therapeutics AG</issuerName>
        <issuerTradingSymbol>CRSP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001456590</rptOwnerCik>
            <rptOwnerName>Versant Venture Capital IV, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE SANSOME STREET, SUITE 3630</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001456591</rptOwnerCik>
            <rptOwnerName>Versant Side Fund IV, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE SANSOME STREET, SUITE 3630</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001589097</rptOwnerCik>
            <rptOwnerName>Versant Venture Capital V, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE SANSOME STREET, SUITE 3630</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001612235</rptOwnerCik>
            <rptOwnerName>Versant Venture Capital V (Canada), LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE SANSOME STREET, SUITE 3630</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94104</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-10-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>95596</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4104045</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-10-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>602</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24334</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-10-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>60219</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2443803</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-10-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4583</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>185987</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These securities are held of record by Versant Venture Capital IV, L.P. (&quot;VVC IV&quot;). Versant Ventures IV, LLC (&quot;VV IV&quot;) is the sole general partner of VVC IV and may be deemed to have voting and investment power over the securities held by VVC IV and as a result may be deemed to have beneficial ownership over such securities. Brian G. Atwood, Samuel D. Colella, Ross A. Jaffe, William J. Link, Rebecca B. Robertson, Bradley Bolzon, Ph.D., Charles M. Warden, Kirk G. Nielsen, Thomas Woiwode and Robin L. Praeger are managing directors of VV IV and share voting and dispositive power over the shares held by VVC IV; however, they each disclaim beneficial ownership of the shares held by VVC IV and VSF IV, except to the extent of their pecuniary interests therein.</footnote>
        <footnote id="F2">These securities are held of record by Versant Side Fund IV, L.P. (&quot;VSF IV&quot;). VV IV is the sole general partner of VSF IV and may be deemed to have voting and investment power over the securities held by VSF IV and as a result may be deemed to have beneficial ownership over such securities. Brian G. Atwood, Samuel D. Colella, Ross A. Jaffe, William J. Link, Rebecca B. Robertson, Bradley Bolzon, Ph.D., Charles M. Warden, Kirk G. Nielsen, Thomas Woiwode and Robin L. Praeger are managing directors of VV IV and share voting and dispositive power over the shares held by VSF IV; however, they each disclaim beneficial ownership of the shares held by VVC IV and VSF IV, except to the extent of their pecuniary interests therein.</footnote>
        <footnote id="F3">These securities are held of record by Versant Venture Capital V, L.P. (&quot;VVC V&quot;). Versant Ventures V, LLC (&quot;VV V&quot;) is the sole general partner of VVC V and may be deemed to have voting and investment power over the securities held by VVC V and as a result may be deemed to have beneficial ownership over such securities. Samuel D. Colella, William J. Link, Bradley Bolzon, Ph.D., Robin L. Praeger, Kirk G. Nielson and Thomas Woiwode, Ph.D. are managing directors of VV V and share voting and dispositive power over the shares held by VVC V; however, they each disclaim beneficial ownership of the shares held by VVC V, except to the extent of their pecuniary interests therein.</footnote>
        <footnote id="F4">These securities are held of record by Versant Venture Capital V (Canada) LP (&quot;VVC CAN&quot;). Versant Ventures V (Canada) GP-GP, Inc. (&quot;VV V CAN GP&quot;) is the sole general partner of Versant Ventures V (Canada), L.P. (&quot;VV V CAN&quot;) and VV V CAN is the sole general partner of  VVC CAN. By virtue of such relationships, VV V CAN GP and VV V CAN may be deemed to have voting and investment power over the securities held by VVC CAN and as a result may be deemed to have beneficial ownership over such securities. Samuel D. Colella, William J. Link, Bradley Bolzon, Ph.D., Robin L. Praeger, Kirk G. Nielson and Thomas Woiwode, Ph.D. are managing directors of VV V CAN GP and share voting and dispositive power over the shares held by VVC CAN; however, they each disclaim beneficial ownership of the shares held by VVC CAN, except to the extent of their pecuniary interests therein.</footnote>
        <footnote id="F5">This report on Form 4 is jointly filed by VVC IV, VSF IV, VVC V and VVC CAN. Each of the Reporting Persons disclaims beneficial ownership of the securities reported herein for purposes of Rule 16a-1(a) under the Securities Exchange Act of 1934, as amended (the &quot;Exchange Act&quot;), except to the extent of its pecuniary interest therein, if any. This report shall not be deemed an admission that any such entity is a beneficial owner of such securities for the purpose of Section 16 of the Exchange Act, or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Robin L. Praeger, Managing Director of Versant Ventures IV, LLC, general partner of Versant Venture Capital IV, L.P.</signatureName>
        <signatureDate>2016-10-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Robin L. Praeger, Managing Director of Versant Ventures IV, LLC, general partner of Versant Side Fund IV, L.P.</signatureName>
        <signatureDate>2016-10-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Robin L. Praeger, Managing Director of Versant Ventures V, LLC, general partner of Versant Venture Capital V, L.P.</signatureName>
        <signatureDate>2016-10-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Robin L. Praeger, Managing Director of Versant Ventures V GP-GP (Canada), Inc., general partner of Versant Ventures V (Canada), L.P., the general partner of Versant Venture Capital V (Canada) LP</signatureName>
        <signatureDate>2016-10-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
