In my PhD I explored how time series analysis can be used to understand the behaviour of complex systems. My focus was two-fold. Firstly, some systems encounter ‘tipping points’ where they suddenly change their behavior. Examples include species extinction or the disappearance of ice sheets. I demonstrated how time series of the system may contain information about the weak spots in the system, i.e. which species is most likely to initiate the extinction or which location of the ice sheet will melt the quickest. Secondly, some systems are chaotic, meaning that they are highly unpredictable. I used statistical methods specifically designed for chaotic systems to quantify complexity in physiological data and to detect causal links in the carbon cycle during the glacial-interglacial cycles of the past 800,000 years.