Extratropical cyclones and their associated extreme precipitation and wind cause large damage and loss of life over Europe. When such extremes occur at the same time and same place they can cause even greater risks. Knowing more about the frequency and spatial pattern of these extremes over Europe and their relationship to cyclones is important for forecasting, the (re)insurance industry and emergency planners. This thesis takes both an Eulerian and a Lagrangian perspective to investigate compound precipitation and wind extremes over Europe and within cyclones. Observational data including ERA5 as well as a high resolution climate model, GloSea5, is used to do this. Over Europe high co-occurrence is found over western coasts and low co-occurrence is found over eastern coasts. These results are found to be robust over different timescales and datasets. Cyclones are found to be strongly associated with compound extremes, given an extreme co-occurring event the chance of a cyclone being nearby is more than 70% for much of Europe. Using an objective feature tracking method, insight into the frequency, spatial pattern and footprint size of extremes within cyclones from a Lagrangian perspective is given. Wind extreme footprints have almost double the area of precipitation and are 5 times larger than compound. The spatial pattern of extremes does not vary much during a cyclones lifecycle, however, the frequency does. The frequency of extreme wind peaks at maximum intensity, within the cold conveyor belt to behind the cold front. The frequency of precipitation and compound extremes peak 6 hours before maximum intensity, ahead of the cyclone centre, in the warm conveyor belt and warm front. The spatial structure of extremes within cyclones are very consistent and vary little with seasonality, intensity and speed. The frequency of extremes and footprint size however varies largely. GloSea5 is evaluated against ERA5, to find out how well it can represent extremes from both an Eulerian and Lagrangian perspective and to be used to investigate unprecedented extremes using the UNSEEN method. Substantial differences in magnitude are found between precipitation and wind extremes between the datasets, however, compound extremes compare well spatially over Europe. GloSea5 represents the general structure of extremes within cyclones well. However, extremes at the cyclone centre tend to be overestimated and regions with the largest frequencies of extremes are underestimated, particularly within cyclones at maximum intensity. Despite biases in GloSea5 it is shown to have a reasonable representation of the storm tracks over Europe and the North Atlantic and can simulate the variability in cyclone frequency well. Although GloSea5 underestimates the number of storms over Europe there are still winters in GloSea5 with unprecedented number of storms for some locations. Extreme storm seasons over Europe and over particular locations arise from a variety of winter mean circulation types. GloSea5 has shown that it can replicate circulation patterns that appear feasible in and similar to the real world. Stormy seasons in GloSea5 are found that produce circulation patterns that are unrealised in the observational record. These large scale dynamics drive large numbers of storms over Central and Southern Europe. GloSea5 represents the size of extreme wind, precipitation and compound footprints very well. It is possible in the current climate to get storms with footprints of extremes almost double the size of that seen historically.