Buoyancy-driven flows are one of the most common sources of turbulence and magnetic field generation in planets and stars. Understanding these systems remains difficult, however, due to the vast range of spatial and temporal scales that characterize them. Numerical simulations of the full governing equations is of limited utility given the inability to access realistic parameter values (e.g. the Reynolds number) and flow regimes. An alternative modelling effort that helps to overcome these limitations is to develop simplified, or reduced, equation sets that focus only on the dynamical scales of interests. Development of reduced equations relies on the mathematical tools provided by multiscale asymptotics, whereby a small (or large) parameter that characterizes the dynamical processes of interest is identified, and the unknown quantities are expanded in a perturbation series about a basic state. In the case of the rotating convection, this basic state is a balance between the pressure and Coriolis forces in the governing equations, well-known as the geostrophic balance. I will discuss how we are using numerical simulations of the new quasi-geostrophic models for understanding convection in planetary atmospheres, oceans, liquid cores, and the convecting regions of stars.