An attempt is made to provide a sound basis for a quantitative theory of cathodoluminescence. Previous theories have neglected the marked scattering of primary electrons by elastic and inelastic collisions, and the effects of this on secondary emission and distribution of secondary electrons responsible for luminescence excitation in the phosphor. Particular attention is given to the detailed processes involved in penetration of the primary particles and to the question of the ultimate limits of cathodoluminescence efficiencies. The latter are shown to be determined by the non-radiative energy transitions of thermal velocity secondary electrons. It appears that the theoretical limit has already been approached in practice.