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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-01-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000098246</issuerCik>
        <issuerName>TIFFANY &amp; CO</issuerName>
        <issuerTradingSymbol>TIF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001202277</rptOwnerCik>
            <rptOwnerName>COSTLEY GARY E</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>2018-01-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3860</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.37</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14822</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2477</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>70.28</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17299</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2878</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>61.12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20177</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock $.01 Par</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9215</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>109.3305</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10962</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>42.37</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-01-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3860</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2020-05-20</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3860.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>70.28</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-01-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2477</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-05-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2477.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>61.12</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-01-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2878</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2022-05-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock $.01 Par</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2878.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F8"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 9,962 restricted stock units, 9,029 of which are vested and 933 of which will vest on the earlier of May 25, 2018, or the termination of the reporting person's service as a director due to death or disability.</footnote>
        <footnote id="F2">The price in Column 4 is a weighted average price. The price actually received ranged from $109.3301 to $109.3400 per share. The reporting person's broker has provided to the issuer and the issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares sold at each price within the range.</footnote>
        <footnote id="F3">Options granted pursuant to the Tiffany &amp; Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16b-3, on May 20, 2010. The option vested in full on the first business day following the grant date.</footnote>
        <footnote id="F4">Total grant 3,860 shares.  0 shares previously exercised.</footnote>
        <footnote id="F5">Options granted pursuant to the Tiffany &amp; Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16b-3, on May 19, 2011. The option vested in full on the grant date.</footnote>
        <footnote id="F6">Total grant 2,477 shares.  0 shares previously exercised.</footnote>
        <footnote id="F7">Granted Pursuant to the Tiffany &amp; Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16(b)-3, on May 17, 2012.  The option vested in full on the grant date.</footnote>
        <footnote id="F8">Total grant 2,878 shares.  0 shares previously exercised.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John C. Duffy, Attorney-in-Fact</signatureName>
        <signatureDate>2018-01-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-01-24
0
0000098246
TIFFANY & CO
TIF
0001202277
COSTLEY GARY E
TIFFANY & CO.
727 FIFTH AVENUE
NEW YORK
NY
10022
1
0
0
0
Common Stock $.01 Par
2018-01-24
4
M
0
3860
42.37
A
14822
D
Common Stock $.01 Par
2018-01-24
4
M
0
2477
70.28
A
17299
D
Common Stock $.01 Par
2018-01-24
4
M
0
2878
61.12
A
20177
D
Common Stock $.01 Par
2018-01-24
4
S
0
9215
109.3305
D
10962
D
Non-Qualified Stock Option (Right to Buy)
42.37
2018-01-24
4
M
0
3860
0
D
2020-05-20
Common Stock $.01 Par
3860.0
0
D
Non-Qualified Stock Option (Right to Buy)
70.28
2018-01-24
4
M
0
2477
0
D
2021-05-19
Common Stock $.01 Par
2477.0
0
D
Non-Qualified Stock Option (Right to Buy)
61.12
2018-01-24
4
M
0
2878
0
D
2022-05-17
Common Stock $.01 Par
2878.0
0
D
Includes 9,962 restricted stock units, 9,029 of which are vested and 933 of which will vest on the earlier of May 25, 2018, or the termination of the reporting person's service as a director due to death or disability.
The price in Column 4 is a weighted average price. The price actually received ranged from $109.3301 to $109.3400 per share. The reporting person's broker has provided to the issuer and the issuer will provide any security holder of the issuer or the SEC staff, upon request, information regarding the number of shares sold at each price within the range.
Options granted pursuant to the Tiffany & Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16b-3, on May 20, 2010. The option vested in full on the first business day following the grant date.
Total grant 3,860 shares.  0 shares previously exercised.
Options granted pursuant to the Tiffany & Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16b-3, on May 19, 2011. The option vested in full on the grant date.
Total grant 2,477 shares.  0 shares previously exercised.
Granted Pursuant to the Tiffany & Co. 2008 Directors Equity Compensation Plan, which complies with Rule 16(b)-3, on May 17, 2012.  The option vested in full on the grant date.
Total grant 2,878 shares.  0 shares previously exercised.
/s/ John C. Duffy, Attorney-in-Fact
2018-01-25