We report on the study of terahertz radiation-induced MIRO-like oscillations of magnetoresistivity in GaAs heterostructures. Our experiments provide an answer on two most intriguing questions-effect of radiation helicity and the role of the edges-yielding crucial information for an understanding of the MIRO (microwave-induced resistance oscillations) origin. Moreover, we demonstrate that the range of materials exhibiting radiation-induced magneto-oscillations can be largely extended by using high-frequency radiation.