Stars over essentially the whole mass domain can become pulsationally unstable during various stages of their evolution. They will appear as variable stars with characteristics that are of much diagnostic value to astronomers. The analysis of such observations provides a challenging and unique approach to study aspects of the internal constitution and evolutionary status of these objects that are not accessible otherwise. This review touches on most classes of known pulsating variable stars and tries to elucidate connections to stellar physical aspects. To aid future investigations, we stress questions and problems that we believe are yet to be resolved satisfactorily.