We introduce OpenEyeSim, a detailed three-dimensional biomechanical model of the human extraocular eye muscles including a visualization of a virtual environment. The main purpose of OpenEyeSim is to serve as a platform for developing models of the joint learning of visual representations and eye-movement control in the perception–action cycle. The architecture and dynamic muscle properties are based on measurements of the human oculomotor system. We show that our model can reproduce different types of eye movements. Additionally, our model is able to calculate metabolic costs of eye movements. It is also able to simulate different eye disorders, such as different forms of strabismus. We propose OpenEyeSim as a platform for studying many of the complexities of oculomotor control and learning during normal and abnormal visual development.