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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-09-21</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>2015-09-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>750</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>79.237</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9359</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price in Column 4 is a weighted average price. The actual purchase prices ranged from $79.237 to $79.239 per share. The reporting person's broker has provided to the issuer and issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares purchased at each price within the range.</footnote>
        <footnote id="F2">848 shares in the total are unvested restricted stock units.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John C. Duffy, Attorney-in-Fact</signatureName>
        <signatureDate>2015-09-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2015-09-21
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
2015-09-21
4
P
0
750
79.237
A
9359
D
The price in Column 4 is a weighted average price. The actual purchase prices ranged from $79.237 to $79.239 per share. The reporting person's broker has provided to the issuer and issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares purchased at each price within the range.
848 shares in the total are unvested restricted stock units.
/s/ John C. Duffy, Attorney-in-Fact
2015-09-22