As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the microscopic origin of macroscopic mechanical behaviours. We first introduce different simulation methods, which we regard as techniques for numerical experimentation, in connection with micromechanical models for intergranular contacts. We lay special emphasis on the important issue of sample representativity and stress the usefulness of dimensional analysis in the definition of relevant control parameters. We then apply this approach to two important rheological regimes of granular systems: solid-like, slowly strained granular materials, which might be ruled by elastoplastic constitutive relations; and liquid-like, dense granular flows, either confined or with a free surface, described by suitable friction and dilatancy laws