This paper presents a review of the main ozone destroying catalytic cycles operating in the stratosphere. Particular attention is paid to the kinetic aspects of these cycles such as the rate limiting step and chain length. Although it is an important kinetic parameter, the chain length of the various cycles is seldom considered when the various catalytic cycles are discussed. This survey highlights that in the low stratosphere the cycles involving HO2 and halogens (notably bromine) are particularly important. In approximate order of effectiveness the most important ozone loss cycles in the polar lower stratosphere are the BrO/CIO, HO2/BrO, and OH/HO2 cycles.