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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-06-01</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>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2020-06-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1246</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20689</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 1,246 unvested restricted stock units, which will vest in accordance with their terms on the earlier of the one-year anniversary of the grant date, or the termination of the reporting person's service as a director due to death or disability.</footnote>
        <footnote id="F2">Given for no consideration.</footnote>
        <footnote id="F3">Includes 12,829 restricted stock units, 10,727 of which are vested; 856 of which are scheduled to vest on the earlier of June 4, 2020, or the termination of the reporting person's service as a director due to death or disability; and 1,246 of which are scheduled to vest on the earlier of June 1, 2021, or the termination of the reporting person's service as a director due to death or disability. The reporting person has elected to defer delivery of 12,206 restricted stock 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/ Catherine W.H. So, Attorney-in-Fact</signatureName>
        <signatureDate>2020-06-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2020-06-01
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
2020-06-01
4
A
0
1246
0
A
20689
D
Includes 1,246 unvested restricted stock units, which will vest in accordance with their terms on the earlier of the one-year anniversary of the grant date, or the termination of the reporting person's service as a director due to death or disability.
Given for no consideration.
Includes 12,829 restricted stock units, 10,727 of which are vested; 856 of which are scheduled to vest on the earlier of June 4, 2020, or the termination of the reporting person's service as a director due to death or disability; and 1,246 of which are scheduled to vest on the earlier of June 1, 2021, or the termination of the reporting person's service as a director due to death or disability. The reporting person has elected to defer delivery of 12,206 restricted stock 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/ Catherine W.H. So, Attorney-in-Fact
2020-06-03