This paper addresses issues concerning exponential stability and robustness of hybrid systems. Stability conditions using Lyapunov techniques are given. The search for the Lyapunov functions is formulated as a linear matrix inequality (LMI) problem for hybrid systems with affine as well as non-linear vector fields. It is shown how the Lyapunov approach most advantageously also can be used to guarantee stability despite the presence of model uncertainties. Several examples are given to illustrate the theory.