The Hubble Space Telescope (HST) has operated continuously since 1990. During that time, four space shuttle-based service missions were launched, three of which added major observational capabilities. A fifth — SM-4 — was intended to replace key telescope systems and install two new instruments. The loss of the space shuttle Columbia, however, resulted in a decision by NASA not to pursue the SM-4 mission leading to a likely end of Hubble's useful life in 2007-2008. This situation resulted in an unprecedented outcry from scientists and the public. As a result, NASA began to explore and develop a robotic servicing mission; and Congress directed NASA to request a study from the National Research Council (NRC) of the robotic and shuttle servicing options for extending the life of Hubble. This report presents an assessment of those two options. It provides an examination of the contributions made by Hubble and those likely as the result of a servicing mission, and a comparative analysis of the potential risk of the two options for servicing Hubble. The study concludes that the Shuttle option would be the most effective one for prolonging Hubble's productive life.