This chapter presents the basics of the two most used simulation tools in numerical work on both small and large systems, Molecular Dynamics (MD) and Monte Carlo (MC) simulations. Both MD and MC simulations require a realistic Hamiltonian. The easiest situations to handle numerically are those that only involve two-body interactions. Occasionally, one may simplify these interactions more and truncate the range of the potential, thus ignoring the interaction energy for particles that are far apart. In other situations a problem may require that e.g. excited electronic states are included into the dynamics, or that other distinctly quantal effects are considered. Occasionally, such effects can be parametrized in terms of many-body potentials. In any case, for both types of simulations the results of a simulation will in general not be better than the Hamiltonian used.