Both classical and quantum mechanical methods are widely used to simulate the dynamics of chemical reactions and molecular motion. In recent work it has become possible to extend quantum dynamics calculations to larger systems, with up to five atoms and many vibrational/rotational states. Through faster and larger computers, enhancements of computational algorithms, and improvements in methodologies will allow quantum dynamical simulations of even larger systems, such extensions are expected to be rather slow and gradual. Thus, for the foreseeable future, classical trajectories are expected to remain a practical and general approach for simulating the dynamics of molecular processes. The seven chapters in this volume deal with: classical and quantum statistical mechanical simulations of the structures and thermodynamics of clusters; the correspondence between the classical and quantum mechanics of highly excited vibrational states; approximate quantum/classical approaches for simulating proton and electron transfer reactions in the condensed phase, and the transition state dynamics of A-B-C heavy-light-heavy systems; a comparison of classical and quantum mechanical calculations of properties of bimolecular reactions, ranging from state-to-state cross sections to thermal rate constants; and calssical and quantum dynamical studies of photon-induced processes on solid surfaces.