The demand, production, supply and use of biomass in a future world after the depletion of fossil fuels is described. In a world without fossils, the limited biomass harvest is the only carbon source. Supply of food and feed has first priority. Demand, supply and use of biomass as the only carbon raw material for the production of a number of indispensable carbon products are analyzed. Bioenergy via combustion plays a significant, but not a decisive role, because the future energy mix is dominated by other renewables. Despite considerable uncertainties of the long-term assessment, some clear hints for a reasonable further development of biomass technologies can be extracted.