In this review article the author presents some basic problems of computational micromechanics, with particular emphasis on multiple-scale problems and micromechanical models. The following examples and applications are discussed: the bridging of atomistic and continuum scales, with application to nanoindentation and brittle-to-ductile transition; the development of dislocation-based constitutive relations for pure metallic crystals and intermetallic compounds, with applications to fracture of single crystals and bicrystals; the simulation of non-planar three-dimensional crack growth at the microscale; the explicit modelling of fragmentation. Diagrams, figures and numerical results illustrate the material.