The cellular slime mold Dictyostelium discoideum is a fascinating organism, not only for biologists, but also for physicists. Since the Belousov–Zhabotinskii reaction pattern, a well-known non-linear phenomenon in chemistry, was observed during aggregation of Dictyostelium amoebae, Dictyostelium has been one of the major subjects of non-linear dynamics studies. Macroscopic theory, such as continuous cell density approximation, has been a common approach to studying pattern formation since the pioneering work of Turing. Recently, promising microscopic approaches, such as the cellular dynamics method, have emerged. They have shown that Dictyostelium is useful as a model system in biology. The synchronization mechanism of oscillatory production of cyclic adenosine 3′,5′-monophosphate in Dictyostelium is discussed in detail to show how it is a universal feature that can explain synchronization in other organisms.