I will present fsg groups which are a common genralization of stable and definably compact groups. They have been introduced and studied by Hrushovski, Peterzil and Pillay in their work on Pillay's conjecture about groups in o-minimal theories. Fsg groups can be characterized by the existence of an invariant measure satisfying a property called generic stability. In some cases (e.g. o-minimal) those groups are compactly dominated: they admit a quotient which is a compact group and whose Haar measure lifts uniquely to the full group.