Hybrid Monte Carlo
Hybrid Monte Carlo  was originally developed to study problems in lattice field theory. Hybrid Monte Carlo combines the molecular dynamics technique, one of whose virtues is that one can move all of the particles in the system in one go (i.e. one time step) with an acceptance probability of 1, with the Monte Carlo technique. By doing this one can use a "dangerously" large time step, which would be potentially be unstable in a pure molecular dynamics simulation, followed by a Metropolis type check that accepts or rejects the final configuration of the molecular dynamics trajectory.