Over the past few years so-called set-oriented numerical methods have been developed for the numerical study of dynamical systems. These methods do not just allow to compute directly – i.e. by avoiding long term simulations of the underlying system – chain recurrent sets or invariant manifolds but they can also be used to approximate statistical quantities such as natural invariant measures, Lyapunov exponents or almost invariant sets. In this talk an overview about recent accomplishments in this area will be given. In particular, concrete applications of these techniques will be presented, e.g. the design of energy efficient spacecraft trajectories or the construction of reliable global zero finding procedures.