The Rayleigh-Taylor instability (RTI) is a phenomenon with a long history. It appears in laboratory mixing experiments, laser plasma devices and astro-physical phenomena. The RTI in miscible fluids can be modelled by considering the evolution of the gradient of the composition density in a buoyancy-driven turbulent flow. Data first produced in simulations by Livescu & Ristorcelli (2007) (available on the Johns Hopkins Turbulence Database) is analysed in terms of this model which shows extremely rapid growth in the density gradient. In contrast, the RTI also appears in immiscible fluids, particularly in materials science where phase field physicists use the Cahn-Hilliard-Navier-Stokes equations to model this phenomenon. I will present some brief mathematical results on this latter problem.