Complex, high-dimensional systems are often characterized by dynamical bottlenecks, or rare events, that determine the rate of evolution of a given system. As the transition states through the dynamical bottlenecks are often difficult to capture experimentally, theory and computation are useful tools to elucidate transition states. This review describes a set of computational methods that enable the rigorous determination of mechanisms, free energy barriers, and rate constants for activated processes in complex, high-dimensional systems. The transition path sampling method for sampling reactive pathways and a subsequent methodological development, aimless shooting, are reviewed. Likelihood maximization, which is a method to extract the reaction coordinate of an activated process from path sampling data, is discussed in detail. In addition, the equilibrium path sampling approach and the earlier BOLAS approach for determining free energy barriers are examined. These techniques offer a means to access kinetically meaningful results from molecular simulation of activated processes in complex systems.