Dynamic Monte-Carlo simulations form a powerful and easy-to-use tool to study the kinetics of reactions in heterogeneous catalysis. The simulations can be viewed as a numerical method to solve the Master Equation that describes the evolution of the catalyst＇s surface and the adsorbates, and which can be derived from first principles. The rate constants in this equation can be computed using quantum chemical methods. The Master Equation can also be used to derive the macroscopic reaction-rate equations, or reaction-diffusion equations. These equations are often convenient to interpret the results of the simulations. We show how various phenomena in heterogeneous catalysis (point defects, steps, surface reconstruction, lateral interactions, spatially varying surface composition) can be modeled. Numerous efficient algorithms have been developed for doing Dynamic Monte-Carlo simulations, and we discuss which one is the most appropriate for a given process that one wants to simulate. We also discuss some new developments that relate to simulating fast diffusion and large-scale pattern formation. (C)1999 Elsevier Science B.V. All rights reserved.