The topic of vision-based grasping is being widely studied in humans and in other primates using various techniques and with different goals. The fundamental related findings are reviewed in this paper, with the aim of providing researchers from different fields, including intelligent robotics and neural computation, a comprehensive but accessible view on the subject. A detailed description of the principal sensorimotor processes and the brain areas involved is provided following a functional perspective, in order to make this survey especially useful for computational modeling and bio-inspired robotic applications.