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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-10-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000098246</issuerCik>
        <issuerName>TIFFANY &amp; CO</issuerName>
        <issuerTradingSymbol>TIF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001553069</rptOwnerCik>
            <rptOwnerName>Rinaldo Michael D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TIFFANY &amp; CO.</rptOwnerStreet1>
            <rptOwnerStreet2>200 FIFTH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10010</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP-CONTRLR PRINC. ACCTG. OFF</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>No Securities Are Beneficially Owned</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Dividend Equivalent Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-10-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents dividend equivalent units accrued on October 10, 2017 in respect of restricted stock units granted to the reporting person on July 19, 2017 pursuant to the Tiffany &amp; Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3. The dividend equivalent units convert to the issuer's common stock on a one-for-one basis.</footnote>
        <footnote id="F2">The dividend equivalent units will vest proportionately with the underlying restricted stock units to which they relate. The dividend equivalent units credited in respect of the restricted stock units granted on July 19, 2017 will vest in four equal annual installments on July 19, 2018, 2019, 2020 and 2021.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John C. Duffy, Attorney-in-Fact</signatureName>
        <signatureDate>2017-10-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-10-10
0
0000098246
TIFFANY & CO
TIF
0001553069
Rinaldo Michael D
TIFFANY & CO.
200 FIFTH AVENUE
NEW YORK
NY
10010
0
1
0
0
VP-CONTRLR PRINC. ACCTG. OFF
No Securities Are Beneficially Owned
0
D
Dividend Equivalent Units
2017-10-10
4
A
0
4
0
A
Common Stock $.01 Par
4.0
4
D
Represents dividend equivalent units accrued on October 10, 2017 in respect of restricted stock units granted to the reporting person on July 19, 2017 pursuant to the Tiffany & Co. 2014 Employee Incentive Plan, which complies with Rule 16b-3. The dividend equivalent units convert to the issuer's common stock on a one-for-one basis.
The dividend equivalent units will vest proportionately with the underlying restricted stock units to which they relate. The dividend equivalent units credited in respect of the restricted stock units granted on July 19, 2017 will vest in four equal annual installments on July 19, 2018, 2019, 2020 and 2021.
/s/ John C. Duffy, Attorney-in-Fact
2017-10-12