Experimental and theoretical studies on ratchet effects in graphene with a lateral superlattice excited by alternating electric fields of terahertz frequency range are presented. A lateral superlattice deposited on top of monolayer graphene is formed either by periodically repeated metal stripes having different widths and spacings or by interdigitated comblike dual-grating-gate (DGG) structures. We show that the ratchet photocurrent excited by terahertz radiation and sensitive to the radiation polarization state can be efficiently controlled by the back gate driving the system through the Dirac point as well as by the lateral asymmetry varied by applying unequal voltages to the DGG subgratings. The ratchet photocurrent includes the Seebeck thermoratchet effect as well as the effects of "linear" and "circular" ratchets, sensitive to the corresponding polarization of the driving electromagnetic force. The experimental data are analyzed for the electronic and plasmonic ratchets taking into account the calculated potential profile and the near field acting on carriers in graphene. We show that the photocurrent generation is based on a combined action of a spatially periodic in-plane potential and the spatially modulated light due to the near-field effects of the light diffraction.