The highly excited valence electron of an alkali Rydberg atom ranges over incredible distances relative to typical atomic scales. In the cold, dense environment of a Bose-Einstein Condensate this electron can interact with one, two, or many other atoms. This leads to the formation of ultra-long- range Rydberg molecules, which are weakly bound states with dipole moments exceeding those of traditional molecules by several orders of magnitude. In this talk I will discuss the theory of Rydberg molecules and highlight some recent experimental observations of these exotic creatures, and discuss several recent efforts to extend the theory to atoms with two valence electrons and to polyatomic systems. I will conclude with some enthusiastic speculation about how the the long-range anisotropic interactions between Rydberg molecules could explore many-body physics.