This monograph sketches out a broad spectrum of problems (from evolution and metabolism to morphogenesis and biogeographical dynamics) whose solution has been impacted by mathematical models. Each of the selected examples has led to the recognition—and set direction to further study—of certain fundamental but unintuitive properties of biological systems, such as the making and breaking of specific symmetries that underlie morphogenesis. Whether they are long-established or only recently accepted, these models are selected for being thought-provoking and illuminating both the achievements...