The features of oscillating reactions are reviewed. By means of familiar examples and simple kinetic models, the role of nonlinearity, multiplicity of steady states and stability against perturbations is outlined first. The Belousov-Zhabotinsky reaction is then briefly discussed as an example of homogeneous-phase chemical oscillator. The occurrence of oscillations and spatiotemporal patterns in heterogeneous catalysis is described, with particular attention to CO oxidation with O-2 on Pt surfaces as well as on supported catalysts in fixed-bed reactors.