Functional Measurement (FM) has been applied to a variety of settings that can be considered as "extreme" settings; that is, settings involving participants with severe cognitive disabilities or involving unusual stimulus material. FM has, as instance, been successfully applied for analyzing (a) numerosity judgments among children as young as 3 years, (b) area judgment among children and adolescents blind from birth, (c) moral judgment among persons with autism and persons with learning disabilities, (d) performance judgments among completely illiterate peasants living at the border of the Sahara, (f) esthetic emotion associated with music excerpts, and (g) ethical thinking among elderly people who were about to die. The methodological aspects of these studies are presented in great detail and the main findings are discussed. The reasons why FM was successful in uncovering new, sometimes unexpected findings in these settings are discussed, notably: (a) no verbalizations/justifications were asked for; that is, judgment processes were not viewed as intrinsically connected with language, and (b) very concrete, daily life material (concrete scenarios) likely to be understood by everyone was used. (Contains 8 figures.)