The problem of learning is arguably at the very core of the problem of intelligence, both biological and artificial. In this article, we review our work over the last 10 years in the area of supervised learning, focusing on three interlinked directions of research--(1) theory, (2) engineering applications (making intelligent software), and (3) neuroscience (understanding the brain's mechanisms of learnings)--that contribute to and complement each other. Because seeing is intelligence, learning is also becoming a key to the study of artificial and biological vision. In the last few years, both computer vision--which attempts to build machines that see--and visual neuroscience--which aims to understand how our visual system works--are undergoing a fundamental change in their approaches. Visual neuroscience is beginning to focus on the mechanisms that allow the cortex to adapt its circuitry and learn a new task.