This review considers cellular chronobiology and examines, at least in a superficial way, several classes of models and mechanisms that have been proposed for circadian rhythmicity and some of the experimental approaches that have appeared to be most productive. After a brief discussion of temporal organization and the metabolic, epigenetic, and circadian time domains, the general properties of circadian rhythms are enumerated. A survey of independent oscillations in isolated organs, tissues, and cells is followed by a review of selected circadian rhythms in eukaryotic microorganisms, with particular emphasis placed on the rhythm of cell division in the algal flagellate Euglena as a model system illustrating temporal differentiation. In the ensuing section, experimental approaches to circadian clock mechanisms are considered. The dissection of the clock by the use of chemical inhibitors is illustrated for the rhythm of bioluminescence in the marine dinoflagellate Gonyaulax and for the rhythm of photosynthetic capacity in the unicellular green alga Acetabularia. Alternatively, genetic analysis of circadian oscillators is considered in the green alga Chlamydomonas and in the bread mold Neurospora, both of which have yielded clock mutants and mutants having biochemical lesions that exhibit altered clock properties. On the basis of the evidence generated by these experimental approaches, several classes of biochemical and molecular models for circadian clocks have been proposed. These include strictly molecular models, feedback loop (network) models, transcriptional (tape-reading) models, and membrane models; some of their key elements and predictions are discussed. Finally, a number of general unsolved problems at the cellular level are briefly mentioned: cell cycle interfaces, the evolution of circadian rhythmicity, the possibility of multiple cellular oscillators, chronopharmacology and chronotherapy, and cell-cycle clocks in development and aging.