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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-04-02</periodOfReport>

    <issuer>
        <issuerCik>0001135185</issuerCik>
        <issuerName>ATLAS AIR WORLDWIDE HOLDINGS INC</issuerName>
        <issuerTradingSymbol>AAWW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001394268</rptOwnerCik>
            <rptOwnerName>Steen Michael</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ATLAS AIR WORLDWIDE HOLDINGS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>2000 WESTCHESTER AVENUE</rptOwnerStreet2>
            <rptOwnerCity>PURCHASE</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10577</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Sr. VP &amp; CMO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2007-04-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>8840</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8840</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>53.69</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2007-04-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10200</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2014-04-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10200</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10200</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents the maximum number of performance-based shares that may be earned by the reporting person on completion of the performance period ended December 31, 2009.  The target amount is 50% of such shares.  The exact number of shares, if any, that may be earned by the reporting person on completion of such performance period is subject to the satisfaction of certain growth-related performance factors over a three-year period relative to a peer group selected by the registrant.</footnote>
        <footnote id="F2">The option vests in four equal annual installments on April 2, 2008, 2009, 2010 and 2011.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Michael W. Borkowski, Attorney-in-Fact</signatureName>
        <signatureDate>2007-04-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
