Many environmental stressors elicit biphasic effects from single cells. Such cellular hormesis may be interpreted in terms of (a) the superimposition of simple biochemical processes or (b) the non-specific behaviour of the cell. The latter approach is emphasized in this article and identified with the universal cell response (UCR); however, the importance of identifying molecular-level concomitants of the UCR is also acknowledged. One difficulty is that when the dose of ligand is very low, mass-action assumptions become invalid and reliable analysis of receptor-ligand interactions requires knowledge of the binding mechanism; this difficulty is discussed. The UCR (cellular hormesis) and its possible underlying mechanisms are considered in the framework of a general scheme of cell life, which logically implies cellular homeostasis or homeorhesis. This framework may be particularly helpful for elucidating and perhaps quantifying conditioning hormesis (adaptation to stressors). The findings of studies on the UCR cannot be extrapolated unequivocally to hormesis in whole organisms or populations and cellular-level hormesis cannot be inferred from whole-organism hormesis. Nevertheless, it has been argued that a better understanding of the underlying cellular mechanisms, i.e., of the UCR, may facilitate the analysis of whole-organism and population data.