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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-01-10</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>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>179139</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <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 $.01 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>Dividend Equivalent Units</value>
                <footnoteId id="F4"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-01-10</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="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 2,202 restricted stock units, 1,269 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">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, Fay 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">Registrant's transfer agent maintains a direct stock purchase program for Registrant's stockholders with a dividend reinvestment feature.  Accordingly, pursuant to Rule 16a-11, dividend equivalent units will no longer be reported on a Form 4 at the time of accrual.</footnote>
        <footnote id="F5">Represents dividend equivalent units accrued on January 10, 2018 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="F6">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 the 1,269 vested 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 he 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>2018-01-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-01-10
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
179139
D
Common Stock $.01 Par
107500
I
By KJC Ltd.
Common Stock $.01 Par
32210
I
By Article IV Trust
Dividend Equivalent Units
2018-01-10
4
A
0
5
0
A
Common Stock $.01 Par
5.0
18
D
Includes 2,202 restricted stock units, 1,269 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.
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, Fay Shutzer, is the sole trustee of the trust.  Reporting person disclaims beneficial ownership of the Tiffany & Co. stock held by the trust.
Registrant's transfer agent maintains a direct stock purchase program for Registrant's stockholders with a dividend reinvestment feature.  Accordingly, pursuant to Rule 16a-11, dividend equivalent units will no longer be reported on a Form 4 at the time of accrual.
Represents dividend equivalent units accrued on January 10, 2018 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 the 1,269 vested 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 he 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
2018-01-12