Abstract: The characteristic Cauchy problem for linear wave equations consists of imposing initial values for the solution on a characteristic hypersurface instead of initial values for the function and its normal derivative on a spacelike Cauchy hypersurface. After an introduction to wave equations on Lorentzian manifolds we show that this problem is well posed under suitable assumptions. This is joint work with Roger Tagne Wafo and it extends classical results by Hörmander.