Graves orbitopathy, also known as thyroid eye disease or thyroid-associated orbitopathy, is visually disabling, cosmetically disfiguring and has a substantial negative impact on a patient's quality of life. There is increasing awareness of the need for early diagnosis and rapid specialist input from endocrinologists and ophthalmologists. Glucocorticoids are the mainstay of treatment; however, recurrence occurs frequently once these are withdrawn. Furthermore, in >60% of cases, normal orbital anatomy is not restored, and skilled rehabilitative surgery is required. Clinical trials have shown that considerable benefit can be derived from the addition of antiproliferative agents (such as mycophenolate or azathioprine) in preventing deterioration after steroid cessation. In addition, targeted biologic therapies have shown promise, including teprotumumab, which reduces proptosis, rituximab (anti-CD20), which reduces inflammation, and tocilizumab, which potentially benefits both of these parameters. Other strategies such as orbital radiotherapy have had their widespread role in combination therapy called into question. The pathophysiology of Graves orbitopathy has also been revised with identification of new potential therapeutic targets. In this Review we provide an up-to-date overview of the field, outline the optimal management of Graves orbitopathy and summarize the research developments in this area to highlight future research questions and direct future clinical trials.