The investigation of the human oculomotor system by eye movement recordings provides an approach to behavior and its alterations in disease. The neurodegenerative process underlying parkinsonian syndromes, including Parkinson’s disease (PD), progressive supranuclear palsy (PSP), and multisystem atrophy (MSA) changes structural and functional brain organization, and thus affects eye movement control in a characteristic manner. Video-oculography has been established as a non-invasive recording device for eye movements, and systematic investigations of eye movement control in a clinical framework have emerged as a functional diagnostic tool in neurodegenerative parkinsonism. Disease-specific brain atrophy in parkinsonian syndromes has been reported for decades, these findings were refined by studies utilizing diffusion tensor imaging (DTI) and task-based/task-free functional MRI—both MRI techniques revealed disease-specific patterns of altered structural and functional brain organization. Here, characteristic disturbances of eye movement control in parkinsonian syndromes and their correlations with the structural and functional brain network alterations are reviewed. On this basis, we discuss the growing field of graph-based network analysis of the structural and functional connectome as a promising candidate for explaining abnormal phenotypes of eye movement control at the network level, both in health and in disease.