After Saccharomyces cerevisiae cells cultured in a medium with glucose consume glucose, the sub-populations of quiescent and non-quiescent cells develop in the budding yeast culture. An age-related chronology of quiescent and non-quiescent yeast cells within this culture is discussed here. We also describe various hallmarks of quiescent and non-quiescent yeast cells. A complex aging-associated program underlies cellular quiescence in budding yeast. This quiescence program includes a cascade of consecutive cellular events orchestrated by an intricate signaling network. We examine here how caloric restriction, a low-calorie diet that extends lifespan and healthspan in yeast and other eukaryotes, influences the cellular quiescence program in S. cerevisiae. One of the main objectives of this review is to stimulate an exploration of the mechanisms that link cellular quiescence to chronological aging of budding yeast. Yeast chronological aging is defined by the length of time during which a yeast cell remains viable after its growth and division are arrested, and it becomes quiescent. We propose a hypothesis on how caloric restriction can slow chronological aging of S. cerevisiae by altering the chronology and properties of quiescent cells. Our hypothesis posits that caloric restriction delays yeast chronological aging by targeting four different processes within quiescent cells.