The phenomena of oscillations, travelling waves, and chaos in reacting chemical systems began as curiosities but now support an active, international research field. This book shows how these 'exotic' patterns arise from the underlying chemical mechanisms. The origin of 'chemical feedback' is revealed using three example reactions: the iodate-reductant (Landolt) reaction, the Belousov-Zhabotinsky reaction, and the combustion of hydrogen. Thermal feedback is also discussed. These mechanisms lead to clock reactions and travelling reaction fronts, thermal runaway, and flames; to oscillations and excitability; to target patterns, spiral and scroll waves; to bistability, ignition, extinction, and hysteresis; and to complex oscillations and chaos in flow reactors. These phenomena are related to important processes in biology, including the development of cardiac arrhythmias, nerve signal transmission, and animal coat patterning.