Abstract: Douady's rabbit is a complex quadratic polynomial whose critical point is periodic of length 3. If we perform a number of Dehn twists around the rabbit's "ears," the resulting map will be combinatorially equivalent, by a theorem of Thurston, to a unique rational map with the same post-critical picture. There are 3 possibilities for this map: the rabbit itself, the corabbit, and the airplane. Determining which of these is the map in question is called the Twisted Rabbit Problem. We present the problem in more detail as well as Bartholdi and Nekrashevych's (2006) solution using iterated monodromy groups.