Magnetic resonance imaging (MRI) now enables precise visualization of the mechanical state of the living human orbit. Resulting insights have motivated histological re-examination of human and simian orbits, providing abundant consistent evidence for the active pulley hypothesis, a re-formulation of ocular motor physiology. Each extraocular muscle (EOM) consists of a global layer (GL) contiguous with the tendon and inserting on the eyeball, and a similar-sized orbital layer (OL) inserting on a connective tissue ring forming the EOM pulley. The pulley controls the EOM path and serves as the EOM's functional origin. Activity of the OL positions the pulley along each rectus EOM to assure that its pulling direction shifts by half the change in ocular orientation, the half-angle behavior characteristic of a linear ocular motor plant. Half-angle behavior is equivalent to Listing's law of ocular torsion, and makes 3-D ocular rotations effectively commutative. Pulleys are configured to maintain oblique EOM paths orthogonal to half-angle behavior, and violate Listing's law during the vestibulo-ocular reflex. Rectus pulley positions shift during convergence, facilitating stereopsis. Innervations, fiber types, and metabolism of the OL and GL differ, consistent with the elastic loading of the former, and viscous loading of the latter. Disorders of the location and stability of rectus pulleys are associated with predictable patterns of incomitant strabismus that may mimic cranial nerve palsies. Surgical interventions improve defective pulley function. Understanding of ocular motor control requires characterization of the behavior of the EOM pulleys as well as knowledge of angular eye orientation.