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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-11-05</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001496671</issuerCik>
        <issuerName>Calithera Biosciences, Inc.</issuerName>
        <issuerTradingSymbol>CALA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001892413</rptOwnerCik>
            <rptOwnerName>Kuriakose Emil</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CALITHERA BIOSCIENCES, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>343 OYSTER POINT BLVD. #200</rptOwnerStreet2>
            <rptOwnerCity>SOUTH SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94080</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CHIEF MEDICAL OFFICER</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>60467</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>STOCK OPTION (RIGHT TO BUY)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>15.75</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2027-09-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>COMMON STOCK</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>38000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>STOCK OPTION (RIGHT TO BUY)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>5.61</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-10-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>COMMON STOCK</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12667</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>STOCK OPTION (RIGHT TO BUY)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.64</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-01-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>COMMON STOCK</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>21000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>STOCK OPTION (RIGHT TO BUY)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>7.41</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-01-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>COMMON STOCK</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>40000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>STOCK OPTION (RIGHT TO BUY)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.98</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-01-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>COMMON STOCK</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>33375</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 14,089 shares acquired at various dates pursuant to the Company's 2014 Employee Stock Purchase Plan.</footnote>
        <footnote id="F2">Includes 26,961 shares acquired upon the vesting of a restricted stock unit award, net of shares sold to satisfy tax obligations, arising out of the vesting of previously granted restricted stock units.</footnote>
        <footnote id="F3">Includes an aggregate of 19,417 shares of common stock to be acquired upon the vesting of Restricted Stock Unit awards granted to the Reporting Person. The Restricted Stock Units shall vest as follows: a) 7,417 restricted stock units shall vest according to the following schedule: one-fourth (1/4th) of the shares subject to the Restricted Stock Unit award will vest each year after January 20, 2021 until the Restricted Stock Units are fully vested,  b) 12,000 restricted stock units shall fully vest on January 3, 2022. The Restricted Stock Units shall be subject to accelerated vesting as set forth in the Reporting Person's employment agreement with the Company.</footnote>
        <footnote id="F4">One-fourth (1/4th) of the Option vests one year after September 29, 2017; the balance of the Option vests in a series of thirty-six (36) successive equal monthly installments thereafter. The Option shall be subject to accelerated vesting as set forth in the Reporting Person's employment agreement with the Company.</footnote>
        <footnote id="F5">One-fourth (1/4th) of the Option vests one year after October 9, 2018; the balance of the Option vests in a series of thirty-six (36) successive equal monthly installments thereafter. The Option shall be subject to accelerated vesting as set forth in the Reporting Person's employment agreement with the Company.</footnote>
        <footnote id="F6">One-fourth (1/4th) of the Option vests one year after January 10, 2019; the balance of the Option vests in a series of thirty-six (36) successive equal monthly installments thereafter. The Option shall be subject to accelerated vesting as set forth in the Reporting Person's employment agreement with the Company.</footnote>
        <footnote id="F7">One-fourth (1/4th) of the Option vests one year after January 17, 2020; the balance of the Option vests in a series of thirty-six (36) successive equal monthly installments thereafter. The Option shall be subject to accelerated vesting as set forth in the Reporting Person's employment agreement with the Company.</footnote>
        <footnote id="F8">One-fourth (1/4th) of the Option vests one year after January 20, 2021; the balance of the Option vests in a series of thirty-six (36) successive equal monthly installments thereafter. The Option shall be subject to accelerated vesting as set forth in the Reporting Person's employment agreement with the Company.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Emil Kuriakose, Name: Emil Kuriakose</signatureName>
        <signatureDate>2021-11-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
