We investigate the miscible Rayleigh–Taylor (RT) instability in both two and three ; dimensions using direct numerical simulations, where the working fluid is assumed ; incompressible under the Boussinesq approximation. We first consider the case of ; randomly perturbed interfaces. With a variety of diagnostics, we develop a physical ; picture for the detailed temporal development of the mixed layer: we identify three ; distinct evolutionary phases in this development, which can be related to detailed ; variations in the growth of the mixing zone. Our analysis provides an explanation ; for the observed differences between two- and three-dimensional RT instability; the ; analysis also leads us to concentrate on the RT models which (i) work equally well for ; both laminar and turbulent flows, and (ii) do not depend on turbulent scaling within ; the mixing layer between fluids. These candidate RT models are based on point sources ; within bubbles (or plumes) and their interaction with each other (or the background ; flow). With this motivation, we examine the evolution of single plumes, and relate our ; numerical results (for single plumes) to a simple analytical model for plume evolution.