Numerical simulations of Rayleigh–Bénard convection in a fluid layer heated from below between two rigid horizontal boundaries have been performed for Rayleigh numbers Ra up to 107, Prandtl numbers in the range between 0.7 and 60 and for aspect ratios $\Gamma$ up to 20. Periodic boundary conditions in the horizontal plane have been used. To a considerable extent, the evolution towards turbulent convection at high values of Ra is governed by processes exhibited by instabilities of steady or time periodic forms of convection at lower Rayleigh numbers. With increasing Ra, the properties of convection are increasingly determined by the thermal boundary layers. The role of mean flows which may be symmetric or antisymmetric with respect to the mid-plane of the layer is emphasized.