The dominant thinking about the interaction between large-scale atmospheric circulations and moist convection holds that convection acts as a heat source for the large-scale circulations, while the latter supply water vapour to the convection. We show that this idea has led to fundamental misconceptions about this interaction, and offer an alternative paradigm, based on the idea that convection is nearly in statistical equilibrium with its environment. According to the alternative paradigm, the vertical temperature profile itself, rather than the heating, is controlled by the convection, which ties the temperature directly to the subcloud-layer entropy. The understanding of large-scale circulations in convecting atmospheres can, therefore, be regarded as a problem of understanding the distribution in space and time of the subcloud-layer entropy. We show that the subcloud-layer entropy is controlled by the sea surface temperature, the surface wind speed, and the large-scale vertical velocity in the convecting layer, and demonstrate how the recognition of this control leads to a simple, physically consistent view of large-scale flows, ranging from the Hadley and Walker circulations to the 30–50-day oscillation. In particular, we argue that the direct effect of convection on large-scale circulations is to reduce by roughly an order of magnitude the effective static stability felt by such circulations, and to damp all of them.