The aim of this talk is to recall the notion of quasi-stationnary distribution and to present a necessary and sufficient criterion for the uniform exponential convergence of conditioned Markov processes to a unique quasi-stationary distribution. While this general criterion can be difficult to check in practical cases, we present new Lyapunov-type criteria which simplify the study of conditioned processes in many situations, including multi-dimensional birth and death processes and diffusion processes conditioned not to vanish. These results have all been obtained in collaboration with Nicolas Champagnat.