Chemical reactions far from equilibrium on solid surfaces may exhibit typical phenomena of nonlinear dynamics, as exemplified by the catalytic oxidation of carbon monoxide on a platinum(110) single-crystal surface. Depending on the external parameters (temperature and partial pressures of the reactants), the temporal variation of the reaction rate may become oscillatory or even chaotic. In a parallel way, the concentration distributions of the adsorbed species on the surface form spatio-temporal patterns including propagating and standing waves, rotating spirals, as well as irregular and rapidly changing structures denoted "chemical turbulence."