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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-07-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001184314</rptOwnerCik>
            <rptOwnerName>BRAVO ROSE MARIE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TIFFANY &amp; CO.</rptOwnerStreet1>
            <rptOwnerStreet2>727 FIFTH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13962</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Dividend Equivalent Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-07-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 9,962 restricted stock units, 9,029 of which are vested and 933 of which will vest on the earlier of May 25, 2018, or the termination of the reporting person's service as a director due to death or disability.</footnote>
        <footnote id="F2">Represents dividend equivalent units accrued on July 10, 2017 in respect of vested restricted stock units granted to the reporting person on May 26, 2016 pursuant to the Tiffany &amp; Co. 2008 Directors Equity Compensation 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="F3">The dividend equivalent units vest proportionately with the underlying restricted stock units to which they relate. The reporting person has elected to defer the maturity date of all the restricted stock units and the related dividend equivalent units (and thereby the delivery of the related shares) until six months after the date on which she ceases to be a director.  The terms of the restricted stock units provide for earlier delivery upon the death, or the end of service as a result of the disability, of the reporting person.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John C. Duffy, Attorney-in-Fact</signatureName>
        <signatureDate>2017-07-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-07-10
0
0000098246
TIFFANY & CO
TIF
0001184314
BRAVO ROSE MARIE
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
13962
D
Dividend Equivalent Units
2017-07-10
4
A
0
5
0
A
Common Stock $.01 Par
5.0
5
D
Includes 9,962 restricted stock units, 9,029 of which are vested and 933 of which will vest on the earlier of May 25, 2018, or the termination of the reporting person's service as a director due to death or disability.
Represents dividend equivalent units accrued on July 10, 2017 in respect of vested restricted stock units granted to the reporting person on May 26, 2016 pursuant to the Tiffany & Co. 2008 Directors Equity Compensation 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 vest proportionately with the underlying restricted stock units to which they relate. The reporting person has elected to defer the maturity date of all the restricted stock units and the related dividend equivalent units (and thereby the delivery of the related shares) until six months after the date on which she ceases to be a director.  The terms of the restricted stock units provide for earlier delivery upon the death, or the end of service as a result of the disability, of the reporting person.
/s/ John C. Duffy, Attorney-in-Fact
2017-07-12