Developmental and school-related changes in basic number, counting, and arithmetic skills from infancy to old age are reviewed. Nearly all of the quantitative competencies that emerge during infancy and the preschool years appear to reflect the operation of a biological primary, or inherent, cognitive system, and appear to be universal in their expression and development. In contrast, most of the basic quantitative competencies acquired in school and that are of importance in industrial societies do not have a direct inherent foundation. As a result, the development of these secondary quantitative abilities varies considerably with educational practices and can, and often does, vary from one country or generation to the next. Variability in the development of secondary quantitative abilities greatly complicates the study of the relation between pathological (e.g., dyscalculia due to stroke) and age-related processes and these abilities.