Extreme events are events that have an extremely low probability of occurring, but often have immense consequences. For this presentation, we focus on extreme events in climate change and wildfires. In the context of climate change, we examine the avoidance of so-called climate tipping points, which are climate regimes where small changes significantly alter the future state of the system. We define a simple climate model, before studying the emission reduction regimes necessary to avoid tipping points. In the context of wildfires, we focus on a phenomenon known as spotting. Spotting refers to the transport of burning pieces of plant material, called firebrands, by wind which, at the time of landing, may ignite new fires beyond the direct ignition zone of the main fire. Spot fires that occur far from the original burn unit are rare but have consequential ramifications since their prediction and control remains challenging. We compare Monte Carlo based methods to Large Deviation Theory when quantifying the landing distribution of firebrands.