New physical and computerized techniques for continuous read-out of intra and intercellular signals allow the study of biochemical dynamics of both local and spreading modes. A vast amount of new information in the area of periodic, quasiperiodic, and chaotic reactions is currently being accumulated, some of which is reviewed here to provide typical mechanisms and occurrences on the basis of a wide variety of reaction circuits and target structures. Following a short review of the time windows of temporal pattern, mechanisms and models of period-generating and transmitting systems are presented for both calcium and oligogenic oscillations. Spreading mechanisms of local signal oscillations through intra- and intercellular space yielding periodic patterns are presented for calcium waves in Dictyostelium discoideum, of cardiovascular and neuronal networks, followed by consideration of some of the properties of complex systems behavior.