The dynamical behavior of many systems arising in physics, chemistry, biology, etc. is dominated by rare but important transition events between long lived states. Important examples include nucleation events during phase transition, conformational changes of macromolecules, or chemical reactions. Understanding the mechanism and computing the rate of these transitions is a topic that has attracted a lot of attention for many years. In this talk, I will discuss some recent theoretical developments for the description of rare events, as well as several computational techniques which allow to determine their pathways and rate. Several examples from material science, chemical kinetics and molecular dynamics will be discussed.

(The movie shows the pathway of collapse of an hydrophobic polymeric chain solvated in a box of 50 thousands explicit water molecules modeled by SPC/E rigid water potential. The regions in white are regions were the water density is below its normal average value, i.e. these are regions where a "bubble" has formed. The results show that the formation of a large bubble around the chain is what drives its collapse. This movie was created by Tommy Miller from Berkeley using the string method.)