Ocular motor diversity exceeds capabilities of only six extraocular muscles (EOMs), but this deficiency is overcome by the plethora of fibers within individual EOMs surpassing requirements of homogeneous actuators. This paper reviews emerging evidence that regions of individual EOMs can be differentially innervated to exert independent oculorotary torques, broadening the oculomotor repertoire, and potentially explaining diverse strabismus pathophysiology. Parallel structure characterizes EOM and tendon fibers, with little transverse coupling of experimentally imposed or actively generated tension. This arrangement enables arbitrary groupings of tendon and muscle fibers to act relatively independently. Coordinated force generation among EOM fibers occurs only upon potentially mutable coordination of innervational commands, whose central basis is suggested by preliminary findings of apparent compartmental segregation of abducens motor neuron pools. Humans, monkeys, and other mammals demonstrate separate, nonoverlapping intramuscular nerve arborizations in the superior vs inferior compartments of the medial rectus (MR) and lateral rectus (LR) EOMs that could apply force at the superior vs inferior portions of scleral insertions, and in the medial vs lateral compartments of the superior oblique that act at the equatorial vs posterior scleral insertions that might preferentially implement incycloduction vs infraduction. Magnetic resonance imaging of the MR during several physiological ocular motor behaviors indicates differential compartmental function. Differential compartmental pathology can influence clinical strabismus. Partial abducens palsy commonly affects the superior LR compartment more than the inferior, inducing vertical strabismus that might erroneously be attributed to cyclovertical EOM pathology. Surgery may selectively manipulate EOM compartments.