This paper suggests that the occupational hierarchy is based on functionally important differences among workers and their jobs and proposes a modified functional theory of occupational stratification. Section I examines the role of education in social stratification. Sections II, III, and IV review (1) functions of schooling, (2) evidence about the relation of intelligence to performance at work and in school, and (3) evidence for the multidimensional nature of job demands. Section V presents new evidence showing that cognitive and non-cognitive demands of work are related to the activities occupations actually require workers to perform and the more difficult jobs tend to be the most critical and prestigious. Section VI provides new evidence that educational requirements for jobs can be explained largely by intelligence demands. Section VII presents a theory of naturally occurring occupational hierarchies. A review of the contributions of previous sections to a modified functional theory is followed by speculations about how occupational hierarchies arise in response to differences in intelligence in a population. The issue of how education relates to these structural processes is explored. Section VIII discusses implications of the theory for educational policy and stratification research. Additional detail about data, tables and figures are appended. (YLB)