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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-05-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001202277</rptOwnerCik>
            <rptOwnerName>COSTLEY GARY E</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>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2014-05-22</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>780</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7912</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>96.73</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-05-22</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2976</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2014-05-23</value>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-05-22</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2976.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2976</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">780 shares in the total are restricted stock units.  The restricted stock units vest 100% on the six-month anniversary of the date of termination (as defined in the grant terms).</footnote>
        <footnote id="F2">Given for no consideration.</footnote>
        <footnote id="F3">6,132 shares in the total are unvested restricted stock units.</footnote>
        <footnote id="F4">Granted pursuant to the Tiffany &amp; Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16(b)-3.  The option is exercisable on the first business day following the grant date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Leigh M. Harlan, Attorney-in-Fact</signatureName>
        <signatureDate>2014-05-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2014-05-22
0
0000098246
TIFFANY & CO
TIF
0001202277
COSTLEY GARY E
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2014-05-22
4
A
0
780
0
A
7912
D
Non-Qualified Stock Option (Right to Buy)
96.73
2014-05-22
4
A
0
2976
0
A
2014-05-23
2024-05-22
Common Stock $.01 Par
2976.0
2976
D
780 shares in the total are restricted stock units.  The restricted stock units vest 100% on the six-month anniversary of the date of termination (as defined in the grant terms).
Given for no consideration.
6,132 shares in the total are unvested restricted stock units.
Granted pursuant to the Tiffany & Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16(b)-3.  The option is exercisable on the first business day following the grant date.
/s/ Leigh M. Harlan, Attorney-in-Fact
2014-05-27