Assessment has been dominated by Classical Test Theory for the last half century although the radically different approach known as Rasch measurement briefly blossomed in England during the 1960s and 1970s. Its open development was stopped dead in the 1980s, whilst some work has continued almost surreptitiously. Elsewhere Rasch has assumed dominance. The purpose of this article is to discuss the major criticisms of the Rasch model, which led to its rejection by some, and to give responses to these criticisms whilst encouraging social scientists to appreciate its strengths. The original breakthrough by Georg Rasch in 1960 has been developed and extended to address every reasonable observational situation in the social sciences.