 He held various positions at the University of Adelaide from 1950 to 1989, including chair of Geology and Palaeontology in 1964.He was an associate at the South Australian Museum from 1953 to 1989.Glaessner received the Lyell Medal of the Geological Society, the Walcott Medal of the National Academy of Sciences in 1982, the Verco Medal awarded by the Royal Society of South Australia (1970), and the Eduard Suess Medal of the Geological Society of Austria (1985).