Extreme weather events pose well-known threats to society regarding elevated mortality, physical and psychological damages, agriculture, and industrial and socioeconomic harm. Understanding and predicting extremes can help to mitigate potential damages. However, extreme weather events are tricky to study as they are rare, complex, and have an unpredictable nature. In this talk, we will try to investigate weather extremes using traditional atmospheric analysis techniques and novel techniques from dynamical system theory. These techniques place different atmospheric variables such as geopotential or precipitation daily maps in phase space and explore the atmospheric behavior around the different states, focusing on areas of interest. We will use the ‘persistence metric’, θ-1, which calculates the mean time the atmosphere stays inside a confined area in the phase space, and the ‘co-occurrence ratio’, α, which evaluates the connection strength of two different atmospheric variables in a shared phase space. We will see how we can use these tools to characterize different atmospheric states, spot extreme weather events, understand the different physical mechanisms behind extremes, and finally predict future changes. First, we will see how we can better understand low-pressure systems that cause extreme wind and precipitation in the Eastern Mediterranean Winter. We will base our analysis on ERA5 at various pressure levels and time lags and evaluate the importance of upper-level support to extreme weather at the surface. Then, we will shift our focus to continental Europe and try to differentiate the projected thermodynamic intensity increase in summer heatwaves from a potential dynamic change caused by climate change. We will use θ-1 on reanalysis data, and different earth system models in different scenarios. Finally, we will discuss the caveats and challenges such as model spread in dynamical system theory techniques.