The eye muscle that elevates the eye is the superior rectus and the muscle that turns the eye laterally is the lateral rectus. There are six muscles in each eye that are responsible for eye movement. They are known as the extraocular muscles.
Lateral movement is known as abduction and involves the eye pulling away from the nose. For the eye to move back toward the nose, the lateral rectus needs to relax so that the medial rectus can contract. A similar action is required by the superior rectus and the superior oblique muscles to elevate and depress the eye.