Earth's atmosphere is constantly convecting. From large cells, providing teleconnections between the tropics and poles, to single isolated clouds, a rich variety of convective events span a range of scales. Often visibly manifest in clouds, convection plays an intricate, not to say leading role in the dynamics of the Earth's weather and climate. Few would argue that the most striking meteorological features encountered on Earth are hurricanes, tornados and tropical storms (all of which invariably involve cumulonimbus convection) and all would recognise that forecasting these systems is a social and economic necessity, as their high wind speeds and potential flash flooding can cause large destruction of infrastructure and, indeed, direct loss of human life. This thesis will focus, in part, on cumulonimbus convection, which occurs due to highly buoyant, localised regions (O(10 kms)) of air punching rapidly upwards, through the troposphere. Strong vertical motions result in phase changes in the water vapour in moist air, which help the observer to notice dramatic, bubbling clouds which can precipitate intensely. Since thermally-driven mixing moves air parcels from the lower to the upper troposphere, meteorologists often refer to cumulonimbus as "deep" convection. But while some aspects of deep convection are well understood, others continue to challenge our understanding.