In our paper we try to describe the basic concepts of chemical waves and spatial pattern formation in a simple way. We pay particular attention to self-organisation phenomena in extended excitable systems. These result in the appearance of travelling waves, spiral waves, target patterns, Turing structures or more complicated structures called scroll waves, which are three-dimensional systems. We describe the most famous oscillating reaction, the Belousov–Zhabotinsky (BZ) reaction, in greater detail. This is because it is of great interest in both physical chemistry and in studies on the evolution and sustenance of self-organising biological systems.