We review recent developments in the theory of supermembranes and their relation to matrix models. Invited talk given at the 31st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, September 2 6, 1997 (to appear in Fortschritte der Physik) and at the CERN Theory Division, December 3, 1997. 1 Supersymmetric quantum mechanics Consider the class of supersymmetric Ham...