The field of psychogerontology is data rich, but theory poor. It will be argued that a constructivist view of science in terms of models or metaphors encourages the development of theories in the field of aging. Historically, there are three psychological models: Age, aging and the aged. The psychology of the aged is concerned with the thematic study of the problematic and non-problematic elderly. The psychology of age focuses on age differences and compares groups of people of different ages. The psychology of aging studies some typicalness of change of average functioning over time. Recent psychological models of aging emphasize degree of variability, rather than average functioning. Primary, secondary and tertiary aging patterns are presented in terms of a differential psychology of aging. A theoretical explanation of the differential aging process will be given in terms of gerodynamics, which lays the foundation of the new branching model of aging.