Excitons consist of an electron bound to a hole (i.e. a missing electron).  By analogy with Cooper pairing in a superconductor, it is easy to imagine that excitons might Bose condense into an unusual collective state.  This phenomenon has finally been observed in a double layer 2D electron system placed in a big magnetic field.  Lots if interesting phenomena attend the condensation and they are the subject of this talk.