<?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>0001112072</rptOwnerCik>
            <rptOwnerName>FARAH ROGER N</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>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Chairman of the Board</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>10355</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>25340</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Family Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 10,355 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 15,339 restricted stock units, 2,836 of which are vested; 2,148 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 10,355 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 the maturity date of all restricted stock 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. The 2,836 vested units include 83 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
0001112072
FARAH ROGER N
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
1
Chairman of the Board
Common Stock $.01 Par
2020-06-01
4
A
0
10355
0
A
25340
D
Common Stock $.01 Par
10000
I
By Family Trust
Includes 10,355 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 15,339 restricted stock units, 2,836 of which are vested; 2,148 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 10,355 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 the maturity date of all restricted stock 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. The 2,836 vested units include 83 accrued dividend equivalent units that were inadvertently omitted from the previously reported total.
/s/ Catherine W.H. So, Attorney-in-Fact
2020-06-03