The characteristics of tropical cyclone intensity and size during the mature stage are presented. Rooted in the classic description by Herbert Riehl, the mature stage is identified as the period from the time of lifetime maximum intensity to the time of lifetime maximum size. This study is the first to analyse the global climatology of the mature stage of tropical cyclones in detail. Three basic features at the mature stage are observed: the reduction of intensity, the outward expansion of the eyewall, and the increase of tangential wind in the outer primary circulation. Globally, about a quarter of tropical cyclones undergo the mature stage. High intensity at the end of the immature stage favours the likelihood of the occurrence of the mature stage. The intensity reduction during the mature stage is considerable with nearly three-quarters of cyclones decreasing by more than 10%, which makes the conventional ‘steady-state’ presumption questionable. The increase in the radius of damaging-force wind is typically about 50 km, while the decrease in maximum wind speed is typically 20% at the mature stage. However, the average integrated kinetic energy and hence destructive potential increases substantially by about 70%. This is consistent with our finding that most of the highly damaging landfalling hurricanes undergo a mature stage. Intensity downgrades during the mature stage may be misinterpreted as they are mostly not accompanied by an overall danger reduction.