We review recent progress in the understanding of the chemical dynamics of gas-surface reactions. Such reactions can involve many dynamically distinct interactions, Our review begins by considering a number of these important elementary processes, dealing in turn with (1) the initial gas-surface interaction including translational, rotational, and vibrational energy exchange, the discussion of vibrational interactions covering both direct vibrational excitation and vibrational relaxation at surfaces; (2) the trapping or adsorption of atoms and molecules on the surface; and (3) the important elementary processes of surface diffusion and desorption. We conclude with a detailed look at two examples of gas-surface reactions, first summarizing what is now known about the dissociative chemisorption of hydrogen at Cu surfaces (and the reverse process of recombinative desorption), Then we describe recent studies of direct gas-surface abstraction (or Eley-Rideal) reactions.