Personality theories often identify sets of primary parts. These are sets of a few personality parts expansive enough to collectively describe the total personality. Examples of such sets include the trilogy of mind (motivation, emotion, and cognition), Freud’s structural set (id, ego, superego), and the recently‐introduced systems set (energy lattice, knowledge works, role player, and executive con‐sciousness). These groups may be of unrecognized importance in understanding human personality. The defining characteristics of such sets are identified, their history is reviewed, their theoretical contributions considered, and then, criteria for distinguishing good from bad sets of primary parts are proposed. Finally, the potential contribution of primary parts sets to personality psychology is revisited.