In the 1970s, studies of tissue architecture and cell proliferation were used to formulate a new model of epidermal homeostasis. This asserted that the tissue was maintained by long-lived, slow-cycling, self-renewing stem cells that generate a short-lived population of transit amplifying (TA) cells, which undergo terminal differentiation after a set number of cell divisions. It was further hypothesized that in the epidermis, the tissue was organized into clonal epidermal proliferative units (EPUs) comprising a central stem cell with surrounding TA cells, which maintain the overlying differentiated cell layers. The stem/TA and EPU hypotheses have been widely influential. Here, we first revaluate older literature, finding numerous studies that conflict with the EPU model. We then review recent large-scale lineage tracing studies in transgenic mice which exclude the stem/TA and EPU hypotheses, and reveal that the epidermis is maintained by a single population of functionally equivalent cycling progenitor cells. The outcome of individual progenitor cell divisions is random, but the probabilities of generating differentiated and progenitor cell daughters are equal, so that homeostasis is maintained across the progenitor population. We reconcile this model with the older literature and place the epidermis in the context of other tissues that are also maintained by continually cycling cells with stochastic fate.