The purpose of this workshop was to identify knowledge gaps in the perioperative management of obstructive sleep apnea (OSA) and obesity hypoventilation syndrome (OHS). A single-day meeting was held at the American Thoracic Society Conference in May, 2016, with representation from many specialties, including anesthesiology, perioperative medicine, sleep, and respiratory medicine. Further research is urgently needed as we look to improve health outcomes for these patients and reduce health care costs. There is currently insufficient evidence to guide screening and optimization of OSA and OHS in the perioperative setting to achieve these objectives. Patients who are at greatest risk of respiratory or cardiac complications related to OSA and OHS are not well defined, and the effectiveness of monitoring and other interventions remains to be determined. Centers involved in sleep research need to develop collaborative networks to allow multicenter studies to address the knowledge gaps identified below.