The ability to control the wavefront of light is fundamental to focusing and redistribution of light, enabling many applications from imaging to spectroscopy. Wave interaction on highly nonlinear photorefractive materials is essentially the only established technology allowing the dynamic control of the wavefront of a light beam with another beam of light, but it is slow and requires large optical power. Here we report a proof-of-principle demonstration of a new technology for two-dimensional (2D) control of light with light based on the coherent interaction of optical beams on highly absorbing plasmonic metasurfaces. We illustrate this by performing 2D all-optical logical operations (AND, XOR and OR) and image processing. Our approach offers diffraction-limited resolution, potentially at arbitrarily-low intensity levels and with 100 THz bandwidth, thus promising new applications in space-division multiplexing, adaptive optics, image correction, processing and recognition, 2D binary optical data processing and reconfigurable optical devices.