I will discuss the formation and Galactic population of ultra-compact binaries. These are binaries with periods shorter than one hour, which means that both components must be compact, evolved stars. The known systems are reviewed, as well as the proposed formation channels. Some open questions are discussed as well as the attempts to answer them. In particular a model for the Galactic population of ultra-compact binaries as optical, X-ray and gravitational-wave sources is shown.