Exophthalmos, also called proptosis, is a bulging of the eye anteriorly out of the orbit (bulging eyes or big eyes). Exophthalmos can be either bilateral (as is often seen in Graves' disease or Thyroid Ophthalmopathy, also called thyroid eye disease) or unilateral (as is often seen in an orbital tumor like cavernous hemangioma or orbital lymphoma or pleomorphic adenoma).