He completed a fellowship in vitreoretinal surgery at the combined program of Oregon Health Sciences University and Devers Eye Institute.
Later he became chairman of the Department of Ophthalmology and Director of the Casey Eye Institute, taking over from Frederick Fraunfelder.
During his tenure as Dean, the entering class size in the medical education program increased from 100 to 120 students.
Robertson became dean of the OHSU School of Medicine in 2003, and in September 2006 became the fourth president of Oregon Health & Science University.
His basic science research focused on the pathophysiology and cellular events related to vitreoretinopathy.
Robertson's other professional interests include the development of healthcare delivery systems and the application of cost accounting principles to medical practice, with the goal of improving the cost-effectiveness of care.
[citation needed] During Robertson's tenure as the university President, the Portland Aerial Tram went into service.