In this paper we review the theory of importance measures for multicomponent binary systems starting out with the classical Birnbaum measure. We then move on to various time independent measures for systems which do not allow repairs including the Barlow and Proschan measure and the Natvig type 1 measure. For the case with repairs we discuss a measure suggested by Barlow and Proschan along with some new suggestions. We also present some new results regarding importance measures for sets of components. In particular we present a generalization and a new representation of the Natvig type 1 set importance measure. We also indicate how the set measures can be extended to the case with repairs.