Glaucoma encompasses a group of neurodegenerative diseases of a progressive nature, causing damage to the ganglion cells of the retina and the upper levels of the visual pathway, which control eyeball mobility. Elevated intraocular pressure is a major risk factor for glaucoma. Despite effective medical and surgical treatments, progressive vision loss is common in glaucoma. There is a need to find a relatively simple diagnostic marker for glaucoma that can be used for screening. Eye movements provide important information about the visual system and related brain structures. This study describes the retinal ganglion cells that are damaged by glaucoma and the impact of this damage on the brain structures that control eye movement. Previous studies have described the presence of eye movement disorders in glaucoma, but the results have been inconclusive. We analyzed the evidence of altered eye movements in glaucoma patients compared with healthy controls, focusing on quantitative eye movement studies measuring saccades and fixation. Evidence shows that fixational eye movements are altered by glaucomatous visual field loss. The measurement of the bivariate contour ellipse area, which describes fixation stability, in glaucoma gives conflicting results depending on the visual task and the measuring device. There was an increase in the latency of saccades and a decrease in amplitude, speed, and accuracy. In addition, it is difficult to inhibit reflex saccade.