In fusion reactor systems, the reaction rates are calculated from a velocity-space integral over the reaction cross section times the distribution functions of the reacting species. In a plasma, the shape of the distribution functions themselves is determined by solving a diffusion-plus-convection problem in velocity space. This review briefly describes the physical processes of central interest to such a description and the mathematical formulation of the problem. It presents the numerical methods used in such calculations by various authors. Optimization on a vector computer (Texas Instruments ASC) is described. Finally, some indication is given as to what may be expected as reactor systems are treated in more detail.