Computational modeling of the primate visual system yields insights of potential relevance to some of the challenges that computer vision is facing, such as object recognition and categorization, motion detection and activity recognition, or vision-based navigation and manipulation. This paper reviews some functional principles and structures that are generally thought to underlie the primate visual cortex, and attempts to extract biological principles that could further advance computer vision research. Organized for a computer vision audience, we present functional principles of the processing hierarchies present in the primate visual system considering recent discoveries in neurophysiology. The hierarchical processing in the primate visual system is characterized by a sequence of different levels of processing (on the order of 10) that constitute a deep hierarchy in contrast to the flat vision architectures predominantly used in today's mainstream computer vision. We hope that the functional description of the deep hierarchies realized in the primate visual system provides valuable insights for the design of computer vision algorithms, fostering increasingly productive interaction between biological and computer vision research.