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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-01-08</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>2014-01-08</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>141309</value>
                    <footnoteId id="F1"/>
                </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="F2"/>
                </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="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>39.75</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-01-08</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2005-01-15</value>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2014-01-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7500.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">979 shares in the total are unvested restricted stock unit grants.</footnote>
        <footnote id="F2">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="F3">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="F4">Options granted under 16(b) Plan on January 15, 2004. The option vested in two equal installments on January 15, 2005 and 2006.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Patrick B. Dorsey, Attorney-in-Fact</signatureName>
        <signatureDate>2014-01-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_138938175457910.xml", "description": "FORM 4", "secsgml_size_bytes": 7505}]
X0306
4
2014-01-08
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
2014-01-08
4
M
0
7500
39.75
A
141309
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)
39.75
2014-01-08
4
M
0
7500
0
D
2005-01-15
2014-01-15
Common Stock
7500.0
0
D
979 shares in the total are unvested restricted stock unit grants.
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.
Options granted under 16(b) Plan on January 15, 2004. The option vested in two equal installments on January 15, 2005 and 2006.
/s/ Patrick B. Dorsey, Attorney-in-Fact
2014-01-10