Professor Thompson's research focuses on the sustainable use of water and other natural resources and on the effective design of regulatory institutions. The author of multiple books on water, the environment, and property, Professor Thompson has published articles on such diverse topics as water markets, fisheries management, biodiversity protection, land conservation, the use of economics and market tools in environmental regulation, and cognitive barriers to resource management.

Thompson is chairman of the board of the Resources Legacy Fund, the Resources Legacy Fund Foundation, the American Farmland Trust, and the Stanford Habitat Conservation Board; a California trustee for The Nature Conservancy; and a board member of both the Sonoran Institute and the Santa Lucia Conservancy. He previously served as a member of the Science Advisory Board for the U.S. Environmental Protection Agency. In 2008, the Supreme Court appointed Thompson to serve as the special master in Montana v. Wyoming (137 Original).