Periodic and transient operation of catalytic CO oxidation reactors has been studied more than any other reaction system. Large increases in global rates of reaction are observed with noble metal catalysts using forced cycling of the feed concentration between oxygen and carbon monoxide at frequencies between 0.02 Hz and 1 Hz. Smaller increases in rate of reaction are seen with metal oxide catalysts with much lower resonance frequencies. We review the past research in the area and outline the challenges and the unanswered questions for future research.