Our study presents a new analysis for a possible transition to a fully sustainable global energy system. It looks in detail at the various energy-using activities within each demand sector, charting their volume and physical energy intensities over time. The approach pays particular attention to maximising energy efficiency through the use of best available technologies. This leads to a reduction in total energy demand and a high share of electricity. The decrease in overall demand is achieved despite a growth in both, population and volume of energy services. The electrification occurs primarily in the Buildings and Transport sectors.We conclude that we can build a global energy system by 2050 which sources 95% of its energy from sustainable sources following an ambitious, but feasible pathway. The pathway is considered achievable because it is based on currently available technology and realistic deployment rates. Policy measures are necessary in all sectors to provide incentives for the transition and we briefly discuss the requirements for these policies. The energy system we propose is robust with respect to (small) variations in the pathway as it only uses a small fraction of each of the sustainable sources.