Glaucoma is a common condition that relies on careful clinical assessment to diagnose and determine disease progression. There is growing evidence that glaucoma is associated not only with loss of retinal ganglion cells but also with degeneration of cortical and subcortical brain structures associated with vision and eye movements. The effect of glaucoma pathophysiology on eye movements is not well understood. In this review, we examine the evidence surrounding altered eye movements in glaucoma patients compared to healthy controls, with a focus on quantitative eye tracking studies measuring saccades, fixation, and optokinetic nystagmus in a range of visual tasks. The evidence suggests that glaucoma patients have alterations in several eye movement domains. Patients exhibit longer saccade latencies, which worsen with increasing glaucoma severity. Other saccadic abnormalities include lower saccade amplitude and velocity, and difficulty inhibiting reflexive saccades. Fixation is pathologically altered in glaucoma with reduced stability. Optokinetic nystagmus measures have also been shown to be abnormal. Complex visual tasks (eg reading, driving, and navigating obstacles), integrate these eye movements and result in behavioral adaptations. The review concludes with a summary of the evidence and recommendations for future research in this emerging field.