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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-04-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001354345</rptOwnerCik>
            <rptOwnerName>Bolzon Bradley J PhD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CRISPR THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>610 MAIN STREET</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02139</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2018-04-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20071</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.00</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1519505</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2018-04-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>589</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>50.60</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>44582</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2018-04-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F6"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>653</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.00</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>49419</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2018-04-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F8"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1528</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.00</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>115645</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F9"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by Versant Venture Capital V, L.P. (&quot;VVC V&quot;).</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $50.00 to $51.59 per share, inclusive. The reporting person undertakes to provide to CRISPR Therapeutics AG, any security holder of CRISPR Therapeutics AG, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the ranges set forth herein.</footnote>
        <footnote id="F3">These securities are held of record by VVC V. 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. The Reporting Person is a managing director of VV V and may be deemed to indirectly beneficially own the securities through his interest in VV V. The Reporting Person disclaims beneficial ownership of such securities, except to the extent of his pecuniary interest therein, if any.</footnote>
        <footnote id="F4">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by Versant Affiliates Fund V, L.P. (&quot;VAF V&quot;).</footnote>
        <footnote id="F5">These securities are held of record by VAF V. VV V is the sole general partner of VAF V and may be deemed to have voting and investment power over the securities held by VAF V and as a result may be deemed to have beneficial ownership over such securities. The Reporting Person is a managing director of VV V and may be deemed to indirectly beneficially own the securities through his interest in VV V. The Reporting Person disclaims beneficial ownership of such securities, except to the extent of his pecuniary interest therein, if any.</footnote>
        <footnote id="F6">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by Versant Ophthalmic Affiliates Fund I, L.P.  (&quot;VOA&quot;).</footnote>
        <footnote id="F7">These securities are held of record by VOA. VV V is the sole general partner of VOA and may be deemed to have voting and investment power over the securities held by VOA and as a result may be deemed to have beneficial ownership over such securities. The Reporting Person is a managing director of VV V and may be deemed to indirectly beneficially own the securities through his interest in VV V. The Reporting Person disclaims beneficial ownership of such securities, except to the extent of his pecuniary interest therein, if any.</footnote>
        <footnote id="F8">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by Versant Venture Capital V (Canada), L.P.
(&quot;VVC CAN&quot;).</footnote>
        <footnote id="F9">These securities are held of record by VVC CAN. Versant Ventures V GP-GP (Canada), 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. 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. The Reporting Person is a director of VV V CAN GP and may be deemed to indirectly beneficially own the shares through his interest in VV V CAN GP. The Reporting Person disclaims beneficial ownership of these shares, except to the extent of his pecuniary interest therein, if any.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Robin L. Praeger, attorney-in-fact</signatureName>
        <signatureDate>2018-04-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
