<?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>0001472082</rptOwnerCik>
            <rptOwnerName>Young Scrivner Annie</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>2758</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 2,748 restricted stock units, 646 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 the 646 vested units (and thereby the delivery of the related shares) until January 1, 2022, and to defer delivery of 623 of the unvested units (and thereby 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 disability, of the reporting person. The 646 vested units include 13 accrued dividend equivalent units that were inadvertently omitted from the previously reported total.</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
0001472082
Young Scrivner Annie
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
2758
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 2,748 restricted stock units, 646 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 the 646 vested units (and thereby the delivery of the related shares) until January 1, 2022, and to defer delivery of 623 of the unvested units (and thereby 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 disability, of the reporting person. The 646 vested units include 13 accrued dividend equivalent units that were inadvertently omitted from the previously reported total.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-06-03