From Observations to Simulations leads us on a journey through the methods used for the scientific analysis of complex systems such as the atmosphere and the Earth system: from meteorology and climatology, as observational sciences, to the development of models and the use of computers as virtual laboratories. In plain, accessible language, avoiding technicalities, but highlighting the conceptually meaningful aspects, the book describes this "Copernican revolution" in meteorology and climatology, a change in methodological paradigm that rigorously tests the definition of some classical concepts, such as "causality" and "prediction." This is the first book that guides the general public (and sets the specialists thinking) through research on complex systems which is contributing to a change in our outlook on nature.