Computer simulation is adding a new dimension to scientific investigation, establishing a role of equal importance with the traditional approaches of experiment and theory. In this paper, we provide a text for understanding the computer simulation methodology of classical statistical mechanics. After developing the theoretical basis of the simulation techniques, the Monte Carlo and Langevin methods and various molecular dynamics methods are described. A very limited discussion is provided on interatomic potential functions, numerical integration schemes, and general simulation procedures for modelling different physical situations and for circumventing excessive computational burdens. The simulation methods are then illustrated using a variety of physical problems studied over the last several years at our laboratory. They include spinodal decomposition of a two-dimensional (2D) fluid, the melting of 2D and quasi-2D films, the structure and energetics of an incommensurate physisorbed film, and the roughening of a silicon solid-melt interface. Finally, we discuss the supercomputer issue, both in terms of super problems for supercomputers and parallel architectures leading to near-future computers that will be one thousand times faster than those currently available. © Taylor & Francis Group, LLC.