Kristen Fichthorn Pennsylvania State University Simulating structural evolution in condensed phases is a considerable current challenge. In many systems, structural evolution occurs via a series of “rare events”, in which the system resides for a long time (compared to the vibrational time scale) in a free-energy minimum before escaping to a neighboring minimum. Currently, many methods exist to characterize escape rates from free-energy minima and rare-event simulation techniques, such as accelerated molecular dynamics and kinetic Monte Carlo, can describe dynamical evolution of a system as a series of jumps between successive free-energy minima. In this tutorial, I will present a review of various methods for rare-event simulation. Examples of these methods will be implemented in Mathematics demos.