**Title:**

Many natural flows are driven by buoyancy forces, perhaps the most familiar being those resulting from density variations due to temperature differences in the presence of a gravitational field: heat rises. The simplest setting to study this sort of system is so-called Rayleigh-Bénard convection, the buoyancy driven flow in a horizontal layer of fluid heated from below and cooled from above. This seminal problem has received tremendous attention over the last century but many riddles remain. In this presentation, following an introduction to the phenomena and its applications along with a review of the current state of theory and experiments on turbulent Rayleigh-Bénard convection, I will describe some light that mathematical analysis has shed on convective transport in recent years.