Binary stars with periods less than one hour contain two evolved objects. These rare systems are of particular interest for understanding binary evolution, for understanding progenitors of supernovae Type Ia, for their contribution to gravitational wave emission at low frequencies, and for the physics of accretion onto compact objects. I will give a short overview of the evolution of binary systems, and in particular leading to very compact settings. The results we have been obtaining in determining the observational characteristics of AM CVn stars will be discussed, as well as the implications for the Galactic population of this type of ultracompact stars. Finally I will look forward to ongoing an upcoming large scale surveys that will provide a substantial multiplication in the number of objects known.