The heterogeneous abilities of the players in various competitive contexts often lead to undesirable outcomes such as low effort provision, lack of diversity, and inequality. A range of policies are implemented to mitigate such issues by enforcing competitive balance, i.e., by leveling the playing field. Some of those policies, known as affirmative action (AA) policies, are practiced in an ethical response to historical discrimination against particular social groups, and are also aimed at increasing competition. This survey summarizes the rapidly growing literature of contest theory on AA and other policies that level the playing field. Using a general theoretical structure, we outline research on contest outcomes under a multitude of such policy mechanisms; and discuss the theoretical, experimental, and empirical findings in relation to some of the common debates surrounding AA.