The nonlinear optical and optoelectronic properties of graphene with the emphasis on the processes of harmonic generation, frequency mixing, photon drag and photogalvanic effects as well as generation of photocurrents due to coherent interference effects, are reviewed. The article presents the state-of-the-art of this subject, including both recent advances and well-established results. Various physical mechanisms controlling transport are described in depth including phenomenological description based on symmetry arguments, models visualizing physics of nonlinear responses, and microscopic theory of individual effects.