As evidence has mounted for the critical role of extraocular muscle (EOM) pulleys in normal ocular motility and disease, opposition to the notion has grown more strident. We review the stages through which pulley theory has developed, distinguishing passive, coordinated, weak differential, and strong differential pulley theories and focusing on points of controversy. There is overwhelming evidence that much of the eye's kinematics, once thought to require brainstem coordination of EOM innervations, is determined by orbital biomechanics. The main criticisms of pulley theory only apply to the strong differential theory, abandoned in 2002. Critiques of the notion of dual EOM insertions are shown to be mistaken. The role of smooth muscle and the issue of rotational noncommutativity are clarified. We discuss how pulley sleeves can be stabilized as required by the theory, noting that more work needs to be done in specifying the tissues involved.