<?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>0001291809</rptOwnerCik>
            <rptOwnerName>Singer Robert S</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>2180</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12486</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 2,180 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 2,140 unvested restricted stock units, 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 2,180 unvested restricted stock units, 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.</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
0001291809
Singer Robert S
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2020-06-01
4
A
0
2180
0
A
12486
D
Includes 2,180 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 2,140 unvested restricted stock units, 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 2,180 unvested restricted stock units, 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.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-06-03