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All teams are named the "Cougars", a name that was first introduced by Eugene L. Roberts in the 1920s, initially only applied to the football team. In 1924, live cougar kittens named Cleo and Tarbo were brought to BYU and used as its mascots. In 1930, Tarbo died and Cleo was sent to the Hogle Zoo in Salt Lake City. By the 1950s all sports teams were known as the Cougars and it was decided that having a person in a costume was a better mascot form than live animals. The athletics mascot, Cosmo the Cougar, was created by Dwayne Stevenson, and made his first appearance before BYU fans on October 15, 1953. The school's fight song is the "Cougar Fight Song".

BYU is owned and operated by the Church of Jesus Christ of Latter-day Saints, and the overwhelming majority of its students are members of that church. Because many of its players serve full-time missions for two years, BYU's athletes are often older on average than other schools' players. The NCAA allows students to serve missions for two years without subtracting that time from their eligibility period. This has caused minor controversy, but is largely recognized as not lending the school any significant advantage, since players receive no athletic and little physical training during their missions. BYU has also received attention from sports networks for refusal to play games on Sunday, as well as disciplining players due to honor code violations.