Roberts attended Stanford University, where he earned his B.A. in 1961 and a Ph.D. in 1968. His doctoral thesis was titled "Studies on the osteology and phylogeny of characoid fishes." He won a 1999 Guggenheim Fellowship in the field of "Organismic Biology & Ecology", and is a research associate at the Smithsonian Tropical Research Institute in Panama and is also affiliated to the Institute of Molecular Biosciences of Mahidol University, Thailand.
Roberts has done extensive fieldwork on tropical freshwater fishes in South America, Africa, Asia, and New Guinea, and has worked in most fish collections in museums and other institutions throughout the world. Fish specimens resulting from this fieldwork are deposited in the California Academy of Sciences, Harvard Museum of Comparative Zoology, Smithsonian Institution, Museum of Zoology of the University of São Paulo, Swedish Museum of Natural History, and many other institutions.
He has published several major works on fish faunas, including the Kapuas River of Borneo, Fly River of New Guinea, and rapids of the lower Congo River, and has described numerous new taxa of freshwater fishes from these and other places. His research also has focused on the major adaptive festures of Ostariophysan fish groups that have facilitated their adaptations and evolutionary radiations. These include the multicuspid teeth of characoids, unicellular epidermal horny projections (named “unculi” by him) in most groups of ostariophysans, and recurrent trophic polymorphism of the lips, horny jaw sheaths, and other soft mouth structures of the Cyprinidae.
Roberts's other scholarly interests include Charles Darwin and his concept of natural selection as products of the Scottish Enlightenment, and identification of royal portrait statues of ancient Khmer devaraja or divine kings with the reigning monarchs they portray including Suryavarman II and Jayavarman VII.