Abstract: Lyapunov functions can characterize many fundamental properties of dynamical systems as attractor-repeller pairs, basins of attraction, and the chain-recurrent set. We discuss an algorithm to compute continuous and piecewise affine (CPA) Lyapunov functions for continuous nonlinear systems by linear optimization. The algorithm can be adapted to compute Lyapunov functions for continuous differential inclusions and discrete systems. We further discuss how the algorithm can be combined with faster methods with less concrete bounds, e.g. the radial-basis-functions collocation method, to deliver true Lyapunov functions comparatively fast.