<p>Converse Lyapunov results express the fact that, for a given dynamical model, the existence of a Lyapunov function is not only a sufficient condition for its stability, but also a necessary criterion. These results provide a solid justification for the Lyapunov approach as a tool to investigate stability, and also make it possible to prove auxiliary robustness properties of dynamical systems. This survey presents converse Lyapunov results concerned with uniform asymptotic stability of dynamical systems in the presence of parametric perturbations, giving a particular emphasis to the infinite-dimensional case.</p>