This lecture describes the statistical mechanics of trajectory space and examples of what can be learned from it. These examples include numerical algorithms for studying rare but important events in complex systems -- systems where transition states are not initially known, where transition states need not coincide with saddles in a potential energy landscape, and where the number of saddles and other features are too numerous and complicated to enumerate explicitly. This methodology for studying trajectories is called "transition path sampling." Extensive material on this topic can be found at this website.