In his three years for the Missouri Tigers baseball team, Crow started 46 games, going 23–8 with a 3.27 earned run average (ERA).

Spending time in both the bullpen and the starting rotation as a freshman, Crow earned his first career victory by throwing a complete game against Pepperdine, staving off elimination in the 2006 NCAA Regional.

[6] He won the Robert A. McNeece Award as the top professional prospect in the 2007 Cape Cod Baseball League season while playing for the Falmouth Commodores.

[10] Crow was selected with the twelfth pick in the first round of the 2009 Major League Baseball Draft by the Kansas City Royals.

To make room for Danny Duffy on the Double A Northwest Arkansas Naturals roster, Crow was demoted to High-A Wilmington on July 31, 2010.

[11] On May 30, 2011, Royals manager Ned Yost announced that Crow had been promoted to the team's closer position on a temporary basis to replace the struggling Joakim Soria.

[14] On November 28, 2014, the Royals traded Crow to the Miami Marlins in exchange for Brian Flynn and Reid Redman.

[15] Crow underwent Tommy John surgery in April 2015 and missed the entirety of the season as a result.