I will present a computational method for simulating the dynamics of atomic systems on time scales much longer than can be accessed with classical dynamics. Possible reaction mechanisms available to the system are found by exploring the potential energy surface from minima to find nearby saddle points. Reaction rates are then calculated using harmonic transition state theory, and the system is propagated in time according to the kinetic Monte Carlo algorithm. The method can be run in parallel, and a distributed computing system has allowed us to simulate dynamics on metal surfaces and in grain boundaries over experimental time scales using an embedded atom potential. The algorithm is efficient enough to model the evolution of systems with ab-initio forces as well, for which I will show a few examples, including metal cluster formation on oxides and catalytic reactions on metal surfaces.