Book excerpt: We present an adaptive importance sampling method for quantifying the statistics of rare-event processes in atomistic simulations. The approach is based on an explicit evaluation of the probability that a sequence of states (or path) initiating in a state A leads to a reactive transition event to final state B. The importance sampling method seeks to bias the sampling of system trajectories such that those that contribute significantly, i.e. those that characterize reactive transitions, are generated more frequently. This is accomplished by means of an importance function, which modifies the transition probabilities among the microstates that comprise a path. For each problem there exists an optimal importance function, which biases that path sampling in such a manner that each path initiating in A leads to a successful event. The fact that the optimal function obeys a variational principle, then leads to an adaptive method in which a trial function form containing a set of adjustable parameters is chosen. The parameters are then adjusted so as to bring the trial function as close as possible to the optimal importance function. We demonstrate the method in two model problems.