One-third of the human cerebral cortex, the layer of gray matter that covers the brain, is devoted exclusively to vision. Many other parts of the brain take part in understanding the visual world and the pattern of connections among all these parts is fairly well known. The big mystery is, what are the neurons saying to each other when we understand what we are seeing and what is the ‘code’ of the trains of electrochemical spikes that carry the information? I will summarize our knowledge of the visual system, give examples of its successes and failures, and describe a computational model of how our brains might sense and understand motion.