This paper reviews our understanding of the role of cumulus convection in hurricanes as well as the various convective parameterization schemes that have been used in hurricane models. Elementary principles show that the primary (tangential) circulation of a vortex intensifies as rings of rotating air converge inward while conserving their (absolute) angular momentum. Thus intensification requires a mechanism to produce enough flow convergence above the surface boundary layer to counter the divergence induced there by the boundary layer itself. Typically, such convergence is associated with the inward branch of the secondary circulation and is produced by an unbalanced negative radial gradient of buoyancy above the boundary layer resulting from condensational heating in the inner region of the vortex. The fact that such buoyancy gradients are produced by all the parameterization schemes, as well as by explicit schemes for latent heat release, explains why all the models are able to simulate hurricane intensification with some degree of realism. In a weak vortex the secondary circulation is dominated by buoyant forcing, but as the vortex intensifies the contribution from surface friction increases until in the mature stage, the buoyantly induced convergence must closely balance the frictionally induced divergence just above the boundary layer. Only a handful of the more recent hurricane models and only two of those in which convection is parameterized represent the effects of convective downdrafts. These downdrafts cool and dry the subcloud layer, tending to suppress further convection, so that acting alone they would serve as a brake on hurricane intensification. The strength of downdrafts decreases when the middle-tropospheric relative humidity increases as a result of sustained cumulus convection over an area. If surface wind speeds are high enough, surface fluxes of sensible and latent heat can more than counteract the cooling and drying effects of convective downdrafts, allowing continued warming of the troposphere in the inner region of the vortex so that vortex intensification can proceed. Accordingly, the surface fluxes provide the energy source for the hurricane, while convection transfers this energy vertically through the troposphere, creating a suitable radial gradient of buoyancy to drive the secondary circulation of the vortex. ¿ 2000 American Geophysical Union