Numerical simulations have become one of the main tools in the research on stellar convection zones and they can be expected to become very important for the study of the convection-diffusion interaction as well. In this review, I will first provide some historical background and then select a few sample problems where numerical simulations of stellar convection have provided useful results or are expected to do so in the near future: solar granulation, interacting convection zones, and semi-convection.