Molecular dynamics (MD) and Monte Carlo (MC) simulations are the two most powerful methods for the investigation of dynamic behavior of atomic and molecular motions of complex systems. To date, such studies have been used to investigate chemical reaction mechanisms, energy transfer pathways, reaction rates, and product yields in a wide array of polyatomic systems. In addition, MD/MC methods have been successfully applied for the investigation of gas-surface reactions, diffusion on surfaces and in the bulk, membrane transport, and synthesis of diamond using chemical vapor deposition (CVD) techniques. The structure of vapor deposited rare gas matrices has been studied using trajectories procedures. If the chemical reaction of interest contains three atoms or fewer, various types of quantum and semiclassical calculations can be brought to bear on the problem. These methods include wave packet studies, close-coupling calculations at various levels of accuracy, and S-matrix theory. Several excellent review articles have been published describing the principal techniques and problems involved in conducting MD studies; the reader may wish to consult these as background material for this discussion. With the advent of relatively inexpensive, powerful personal computers, MD/MC simulations have become routine. Once the potential-energy hypersurface for the system has been obtained, the computations are straightforward, though time-consuming. In the majority of cases, the computational time required is on the order of hours to a few days. However, the accuracy of these simulations depends critically on the accuracy of the potential hypersurface used. The major problem associated with MD/MC investigations is the development of a potential-energy hypersurface whose topographical features are sufficiently close to those of the true, but unknown, surface that the results of the calculations are experimentally meaningful. Once the potential surface is chosen or computed, all the results from any quantum mechanical, semiclassical, or classical scattering or equilibrium calculation are determined. The only purpose of the MD calculations is to ascertain what these results are. Therefore, the most critical part of any MD/MC study is the development of the potential-energy hypersurface and the associated force field.