A two-time Olympian, Leyva earned all-around bronze at the 2012 London Olympic Games and added silver medals on horizontal bar and parallel bars at the Rio Olympic Games four years later. He was a member of the 2011 and 2014 bronze-medal-winning U.S. World Championships teams and also picked up individual gold and silver on parallel bars and silver on horizontal bar in five World Championships appearances between 2009 and 2015.
As a senior, Leyva compiled five World Cup medals and eight U.S. all-around or apparatus titles. At the 2012 U.S. Olympic Team Trials, he bested all competitors in the all-around and on his signature events, high bar, and parallel bars.
Leyva retired following the 2016 Olympics, transitioning his focus to acting and media.