A neuroprosthesis is a type of precision medical device that is intended to manipulate the neuronal signals of the brain in a closed-loop fashion, while simultaneously receiving stimuli from the environment and controlling some part of a human brain or body. Incoming visual information can be processed by the brain in millisecond intervals. The retina computes visual scenes and sends its output to the cortex in the form of neuronal spikes for further computation. Thus, the neuronal signal of interest for a retinal neuroprosthesis is the neuronal spike. Closed-loop computation in a neuroprosthesis includes two stages: encoding a stimulus as a neuronal signal, and decoding it back into a stimulus. In this paper, we review some of the recent progress that has been achieved in visual computation models that use spikes to analyze natural scenes that include static images and dynamic videos. We hypothesize that in order to obtain a better understanding of the computational principles in the retina, a hypercircuit view of the retina is necessary, in which the different functional network motifs that have been revealed in the cortex neuronal network are taken into consideration when interacting with the retina. The different building blocks of the retina, which include a diversity of cell types and synaptic connections—both chemical synapses and electrical synapses (gap junctions)—make the retina an ideal neuronal network for adapting the computational techniques that have been developed in artificial intelligence to model the encoding and decoding of visual scenes. An overall systems approach to visual computation with neuronal spikes is necessary in order to advance the next generation of retinal neuroprosthesis as an artificial visual system.