A review. Since the first mol. dynamics simulations of hard spheres by Alder and Wainwright in the fifties of the last century (Alder, B.J. and Wainwright, T.E. (1957) Phase transition for a hard sphere system, J. Chem. Phys. 27, 1208-1209), this method has evolved to a powerful and intensively used technique in the computer simulations of phys., chem. and biol. systems. The present article is meant as a brief and easy starting point for the very beginner in this field. It gives an introduction to the basic principles of the method and sketches also some of the more elaborate extensions and recent methodol. developments such as first-principles mol. dynamics simulations (Car-Parrinello simulations) and mixed quantum mech./mol. mech. (QM/MM) approaches. A final outlook attempts to summarize the state-of-the-art of what is possible today including the main limitations that presently exist and some of the current strategies of how to overcome them. [on SciFinder (R)]