An exotic group C*-algebra is a C*-algebra that lies naturally between the reduced and the universal group C*-algebra. In this thesis we study the existence of such C*-algebras for the special linear groups over the complex numbers and for the symplectic group, as examples of connected simple Lie groups with real rank greater or equal than 2. In both cases we are able to show the existence of a continuum of exotic group C*-algebras. In joint work with Emilie Elkiær, Maria Gerasimova and Tim de Laat we studied induction of unitary representations from an open subgroup H in a locally compact group G. We observed that in this case exotic group C*-algebras of H give rise to exotic group C*-algebras of G. If H further has the Kunze-Stein property, it is moreover possible to deduce the existence of representations of G with specific integrability properties from the existence of such representations of H.