Starting with the work of Cajal more than 100 years ago, neuroscience has sought to understand how the cells of the brain give rise to cognitive functions. How far has neuroscience progressed in this endeavor? This Perspective assesses progress in elucidating five basic brain processes: visual recognition, long-term memory, short-term memory, action selection, and motor control. Each of these processes entails several levels of analysis: the behavioral properties, the underlying computational algorithm, and the cellular/network mechanisms that implement that algorithm. At this juncture, while many questions remain unanswered, achievements in several areas of research have made it possible to relate specific properties of brain networks to cognitive functions. What has been learned reveals, at least in rough outline, how cognitive processes can be an emergent property of neurons and their connections.