The study of sustainable energy systems is an interdisciplinary endeavour which entails the analysis of a large amount of diverse data and complex interactions that are better understood if developed from first principles. This paper reviews the approaches to this analysis and presents as a general case study, a fossil free imaginary island whose electricity, heat and mobility demand are fulfilled with sustainable and renewable energies only. The detailed hourly balance between supply and demand highlights the importance of energy storage, which is achieved by reversible hydropower and storage in electric vehicles.