Practically everything of interest in the world moves, and even the retinal images of stationary objects move because the eyes are never entirely still. It is therefore not a surprise that the mammalian visual system has evolved a pathway that seems to be devoted to processing visual motion information. In monkeys, neurons in area MT (V5) of the extrastriate visual cortex are all direction-selective, and signal the true motion of complex visual patterns, a response pattern not seen in earlier visual areas. For this and other reasons, MT is thought to have a special role in visual motion processing. Surprisingly, this complex neuronal behavior can be accurately captured by a linear feed-forward model that operates on the outputs of nonlinear directionally-selective V1 cells. This model reveals that the complex response properties of MT cells do not result only from the action of circuits in MT, but depend critically on computations that take place in earlier visual areas such as V1. This suggests that a relatively simple and experimentally tractable architecture may account for the complex transformations of visual information that take place beyond the primary visual cortex, but that evaluating this kind of architecture requires a good understanding of both cortical networks and their inputs. An incidental finding arising from tests of this model suggests, unexpectedly, that despite its central role in visual motion processing, there are important situations in which MT does not contribute to our experience of visual motion.