<?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>0001016750</rptOwnerCik>
            <rptOwnerName>SHUTZER WILLIAM A</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>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>142089</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>107500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By KJC Ltd.</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $0.1 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>32210</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Article IV Trust</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </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="F5"/>
            </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">Given for no consideration.</footnote>
        <footnote id="F2">780 shares in the total are restricted stock units.  The restricted stock units vest 100% on the first anniversary of the grant date.</footnote>
        <footnote id="F3">KJC Ltd. is a Delaware limited partnership of which the reporting person is the sole general partner and of which three of his adult children are limited partners. Reporting person disclaims beneficial ownership of Tiffany &amp; Co. stock held by KJC Ltd.</footnote>
        <footnote id="F4">Article IV trust dated August 1, 2012 for one of the reporting person's adult children.  Reporting person's spouse, Faye Shutzer, is the sole trustee of the trust.  Reporting person disclaims beneficial ownership of the Tiffany &amp; Co. stock held by the trust.</footnote>
        <footnote id="F5">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>
[{"type": "4", "sequence": "1", "filename": "wf-form4_140122646548706.xml", "description": "FORM 4", "secsgml_size_bytes": 7752}]
X0306
4
2014-05-22
0
0000098246
TIFFANY & CO
TIF
0001016750
SHUTZER WILLIAM A
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
142089
D
Common Stock $.01 Par
107500
I
By KJC Ltd.
Common Stock $0.1 Par
32210
I
By Article IV Trust
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
Given for no consideration.
780 shares in the total are restricted stock units.  The restricted stock units vest 100% on the first anniversary of the grant date.
KJC Ltd. is a Delaware limited partnership of which the reporting person is the sole general partner and of which three of his adult children are limited partners. Reporting person disclaims beneficial ownership of Tiffany & Co. stock held by KJC Ltd.
Article IV trust dated August 1, 2012 for one of the reporting person's adult children.  Reporting person's spouse, Faye Shutzer, is the sole trustee of the trust.  Reporting person disclaims beneficial ownership of the Tiffany & Co. stock held by the trust.
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