Greifeld was born in Queens, New York, to an Italian American mother and a father of Irish and German descent.

[5] Under Greifeld, in 2007 Nasdaq attempted a hostile takeover of the London Stock Exchange, but their offer was ultimately rejected by shareholders.

[6] In 2011, Nasdaq OMX collaborated with IntercontinentalExchange to attempt a hostile takeover of NYSE Euronext, however their bid was withdrawn due to antitrust concerns.

[10][12] Greifeld left Virtu in April 2023 to work on launching a tech-focused investment fund, Cornerstone FTM, among other endeavors.

[13][14] Greifeld has resided with his wife and family in Westfield, New Jersey[15][16] In 2016, he gave the commencement address at Iona College.