The investigation of photoelectric phenomena in the terahertz frequency range is a powerful tool to study nonequilibrium processes in low-dimensional structures. In this work, non-linear high frequency transport phenomena in graphene driven by the free-carrier absorption of electromagnetic radiation are explored. It is demonstrated that in the presence of adatoms and/or a substrate, as well as in the vicinity of graphene edges the carriers exhibit a directed motion in response to the alternating electric field of the terahertz radiation. Moreover, it is sown that these photoelectric phenomena can be giantly enhanced if graphene is deposited on a substrate with a negative dielectric constant. Novel models of the photocurrent generation are developed to describe the nonequilibrium processes in the purest two-dimensional material. The experiments together with the theoretical considerations give access to fundamental properties of graphene.