Chemical kinetics plays an important role in controlling the atmospheric composition of all planetary atmospheres, including those of extrasolar planets. For the hottest exoplanets, the composition can closely follow thermochemical-equilibrium predictions, at least in the visible and infrared photosphere at dayside (eclipse) conditions. However, for atmospheric temperatures < ~2000 K, and in the uppermost atmosphere at any temperature, chemical kinetics matters. The two key mechanisms by which kinetic processes drive an exoplanet atmosphere out of equilibrium are photochemistry and transport-induced quenching. We review these disequilibrium processes in detail, discuss observational consequences, and examine some of the current evidence for kinetic processes on extrasolar planets.