For the purposes of this study, any mental processes of behaviors that are common or frequent in a population are defined as normal. The 'creativity' definition used is 'a general cognitive style and personality syndrome involving ideational fluency; conceptual overinclusion; preference for ambiguity, complexity and asymmetric patterns; a tendency to form many and unusual associations; idiosyncratic thinking; odd sensory and perceptual experiences; feelings of restlessness and the inclination toward impulsive outbursts; preference for solitude; rejection of common social values; broad interests; autonomy and independence of judgment; and atttraction to artistic and aesthetic experiences.' 'Criminality' is defined as anxious and emotional expressions accompanied by aggressive outbursts, lawbreaking, and antisocial behavior; and craziness is viewed as a folk concept that describes bizarre, unintelligible thinking and behavior. The literature review reported describes a number of studies indicating an empirical relationship among criminal, creative, and crazy forms of deviance. Possible explanations for this empirical relationship are examined from the perspective of sociobiology (study of the hereditary basis of social behavior). Evidence for a common genetic basis for criminality, creativity, and craziness is considered, along with the role of nonconformity in evolutionary adaptation. The final subsection of the paper considers socioanalytic theory, a comprehensive personality theory designed to explain the role of personality in human evolution. Tabular data and 98 references are provided.