Luca Ghiringhelli Fritz-Haber-Institut der Max-Planck-Gesellschaft The study of rare events is one of the most fundamental problems in chemistry. Chemical reactions and conformation changes of molecules are examples of rare events. These events are rare because the system has to overcome some barriers, which can be of energetic or entropic nature, or both. Transition-state theory relates the evaluation of transition rates of rare events to the search for the so-called minimum-energy path (MEP), i.e., the lowest-energy path for the rearrangement of a group of atoms from one stable configuration to another. In this lecture, I will introduce two main computational techniques for the numerical evaluation of MEPs: the nudged-elastic-band method and the string method, including some of their relevant variations.