A reaction-diffusion computer is a large-scale array of elementary processors, micro-volumes of chemical medium, which act, change their states determined by chemical reactions, concurrently and interact locally, via local diffusion of chemical species; it transforms data to results, both represented by concentration profiles of chemical species, by traveling and colliding waves in spatially extended chemical media. We show that reaction-diffusion processors, simulated or experimental, can solve a variety of tasks, including computational geometry, robot navigation, logics and arithmetics.