Sudden Stratospheric Warmings (SSWs) are extreme dynamical events occurring in the wintertime stratosphere that consist of a reversal of the typical westerly circulation and a simultaneous warming of the polar region by 30-40K over the course of a few days. After these events occur, there is a downward propagation to the troposphere of the wind and temperature anomalies associated with them. This implies that prediction of certain weather variables can be improved on these timescales with knowledge of the occurrence of SSWs in the stratosphere. I will give an introduction to the ideas of stratosphere-troposphere coupling, and discuss the work I have done to understand the structure of the planetary waves that drive SSWs. In particular, I will show that standing waves are primarily responsible for the well-known connection between lower stratospheric wave activity fluxes and fluctuations in the strength of the mid-stratosphere polar vortex. I will discuss the possibility of longer lead-time prediction of SSWs based on knowledge of the standing wave field, and therefore better sub-seasonal prediction of tropospheric Northern Annular Mode related variables.