It is well-known that micro- and nanoparticles can move by phoretic effects in response to externally imposed gradients of scalar quantities such as chemical concentration or electric potential. A class of active colloids can propel themselves through aqueous media by generating local gradients of concentration and electrical potential via surface reactions. Phoretic active colloids can be controlled using external stimuli and can mimic collective behaviors exhibited by many biological swimmers. Low–Reynolds number physicochemical hydrodynamics imposes unique challenges and constraints that must be understood for the practical potential of active colloids to be realized. Here, we review the rich physics underlying the operation of phoretic active colloids, describe their interactions and collective behaviors, and discuss promising directions for future research.