Tropical deep convection with overshooting tops is identified by defining five different reference heights using a 5-year TRMM database. The common properties of these extreme convective systems are examined from a global perspective. It is found that 1.3% of tropical convection systems reach 14 km and 0.1% of them may even penetrate the 380 K potential temperature level. Overshooting convection is more frequent over land than over water, especially over central Africa, Indonesia and South America. The seasonal, diurnal and geodistribution patterns of overshooting deep convection show very little sensitivity to the definition of the reference level. The global distribution of overshooting area, volume and precipitating ice mass shows that central Africa makes a disproportionately large contribution to overshooting convection. A semiannual cycle of total overshooting area, volume and precipitating ice mass is found.