Let $F\colon\mathbb{R}^2 \to \mathbb{R}^2$ be a homeomorphism. An open $F$-invariant subset $U$ of $\mathbb{R}^2$ is a pruning region for $F$ if it is possible to deform $F$ continuously to a homeomorphism $F_U$ for which every point of $U$ is wandering, but which has the same dynamics as $F$ outside of $U$. This concept was motivated by the {\em Pruning Front Conjecture} of Cvitanović, Gunaratne, and Procaccia, which claims that every Hénon map can be understood as a pruned horseshoe. This paper is a survey of pruning theory, concentrating on prunings of the horseshoe. We describe conditions on a disk $D$ which ensure that the orbit of its interior is a pruning region; explain how prunings of the horseshoe can be understood in terms of underlying tree maps; discuss the connection between pruning and Thurston's classification theorem for surface homeomorphisms; motivate a conjecture describing the forcing relation on horseshoe braid types; and use this theory to give a precise statement of the pruning front conjecture.