  Atypical, rare trajectories of dynamical systems are important: they are
often the paths for chemical reactions, the haven of (relative) stability of
planetary systems, the rogue waves that are detected in oil platforms, the
structures that are responsible for intermittency in a turbulent liquid, the
active regions that allow a supercooled liquid to flow... Simulating them in an
efficient, accelerated way, is in fact quite simple.
  In this paper we review a computational technique to study such rare events
in both stochastic and Hamiltonian systems. The method is based on the
evolution of a family of copies of the system which are replicated or killed in
such a way as to favor the realization of the atypical trajectories. We
illustrate this with various examples.
