Oculomotor deficits are common in hereditary ataxia, but disproportionally neglected in clinical ataxia scales and as outcome measures for interventional trials. Quantitative assessment of oculomotor function has become increasingly available and thus applicable in multicenter trials and offers the opportunity to capture severity and progression of oculomotor impairment in a sensitive and reliable manner. In this consensus paper of the Ataxia Global Initiative Working Group On Digital Oculomotor Biomarkers, based on a systematic literature review, we propose harmonized methodology and measurement parameters for the quantitative assessment of oculomotor function in natural-history studies and clinical trials in hereditary ataxia. MEDLINE was searched for articles reporting on oculomotor/vestibular properties in ataxia patients and a study-tailored quality-assessment was performed. One-hundred-and-seventeen articles reporting on subjects with genetically confirmed (n=1134) or suspected hereditary ataxia (n=198), and degenerative ataxias with sporadic presentation (n=480) were included and subject to data extraction. Based on robust discrimination from controls, correlation with disease-severity, sensitivity to change, and feasibility in international multicenter settings as prerequisite for clinical trials, we prioritize a core-set of five eye-movement types: (i) pursuit eye movements, (ii) saccadic eye movements, (iii) fixation, (iv) eccentric gaze holding, and (v) rotational vestibulo-ocular reflex. We provide detailed guidelines for their acquisition, and recommendations on the quantitative parameters to extract. Limitations include low study quality, heterogeneity in patient populations, and lack of longitudinal studies. Standardization of quantitative oculomotor assessments will facilitate their implementation, interpretation, and validation in clinical trials, and ultimately advance our understanding of the evolution of oculomotor network dysfunction in hereditary ataxias.