A number of researchers have proposed models of early motion sensing based on direction-selective, spatiotemporal linear operators. Others have formalized the problem of measuring optical flow in terms of the spatial and temporal derivatives of stimulus intensity. Recently, the spatiotemporal filter models and the gradient-based methods have been placed into a common framework. In this chapter, we review that framework and we extend it to develop a new model for the computation and representation of velocity information in the primate visual system. We use the model to simulate psychophysical data on perceived velocity of sine-grating plaid patterns, physiological data on responses of simple cells in primary (striate) visual cortex, and physiological data on responses of cells in visual area MT.