In classical and quasiclassical trajectory chemical dynamics simulations, the atomistic dynamics of collisions, chemical reactions, and energy transfer are studied by solving the classical equations of motion. These equations require the potential energy and its gradient for the chemical system under study, and they may be obtained directly from an electronic structure theory. This article reviews such direct dynamics simulations. The accuracy of classical chemical dynamics is considered, with simulations highlighted for the F- + CH3OOH reaction and of energy transfer in collisions of CO2 with a perfluorinated self-assembled monolayer (F-SAM) surface. Procedures for interfacing chemical dynamics and electronic structure theory computer codes are discussed. A Hessian-based predictor-corrector algorithm and high-accuracy Hessian updating algorithm, for enhancing the efficiency of direct dynamics simulations, are described. In these simulations, an ensemble of trajectories is calculated which represents the experimental and chemical system under study. Algorithms are described for selecting the appropriate initial conditions for bimolecular and unimolecular reactions, gas-surface collisions, and initializing trajectories at transition states and conical intersections. Illustrative direct dynamics simulations are presented for the Cl- + CH3I SN2 reaction, unimolecular decomposition of the epoxy resin constituent CH3-NH-CH=CH-CH3 versus temperature, collisions and reactions of N-protonated diglycine with a F-SAM surface that has a reactive head group, and the product energy partitioning for the post-transition state dynamics of C2H5F → HF + C2H4 dissociation. © 2012 John Wiley & Sons, Ltd.