Cortical visual prostheses are intended to restore vision by targeted electrical stimulation of the visual cortex. The perception of spots of light, called phosphenes, resulting from microstimulation of the visual pathway, suggests the possibility of creating meaningful percept made of phosphenes. However, to date electrical stimulation of V1 has still not resulted in perception of phosphenated images that goes beyond punctate spots of light. In this review, we summarize the clinical and experimental progress that has been made in generating phosphenes and modulating their associated perceptual characteristics in human and macaque primary visual cortex (V1). We focus specifically on the effects of different microstimulation parameters on perception and we analyse key challenges facing the generation of meaningful artificial percepts. Finally, we propose solutions to these challenges based on the application of supervised learning of population codes for spatial stimulation of visual cortex.