It is known that vergence allows the brain to perceive depth. Although convergence (inward turning of the eyes) and divergence (outward turning of the eyes) movements utilize the same extraocular muscles and visual field, emerging evidence supports that they are different neural control systems. Both adapt (the system's ability to alter its dynamics) and are correlated to phoria (the resting state of the visual system); however the behavior is different depending upon the system. This review discusses the classical and new tools used to analyze vergence movements, the neural control of each system, and its interaction with version. A review of the current models shows that new models are needed to explain these recent behavior studies which will facilitate the understanding of vergence dysfunctions. Eye movement from far to near (convergent movement) or from near to far (divergent movement) are performed quickly and accurately. The convergence and divergence movements appear to be mediated by different neural control processes. For example, while divergence can be faster at near, convergence can be faster at far. The vergence resting level adapts to sustained stimuli and this adaptation can influence the dynamics of both systems. Movement dynamics can also adapt as repetitive movements and alter the peak velocity of each system. However, typical vergence movements in daily living rarely consist of pure symmetrical vergence movements but exhibit a combination of version and vergence movements. Reviewing recent models shows that none adequately describe the influence of phoria, adaptation, the differences between convergence and divergence control and its interaction with version. The development of a new model is needed to describe the neural control of convergence and divergence taking into account the influence of adaptation, phoria and its interaction with the version system. Once this model is developed, it can yield more insight into abnormalities of the vergence system such as convergence and divergence insufficiencies or excess which can develop from numerous neurological dysfunctions.