Inventory calculations have a key role to play in designing future fusion power plants because, for a given irradiation field and material, they can predict the time evolution in chemical composition, activation, decay heat, gamma-dose, gas production, and even damage (dpa) dose. For conceptual designs of the European DEMO fusion reactor such calculations provide information about the neutron shielding requirements, maintenance schedules, and waste disposal prospects; thereby guiding future development. Extensive neutron-transport and inventory calculations have been performed for a reference DEMO reactor model with four different tritium-breeding blanket concepts. The results have been used to chart the post-operation variation in activity and decay heat from different vessel components, demonstrating that the shielding performance of the different blanket concepts – for a given blanket thickness – varies significantly. Detailed analyses of the simulated nuclide inventories for the vacuum vessel (VV) and divertor highlight the most dominant radionuclides, potentially suggesting how changes in material composition could help to reduce activity. Minor impurities in the raw composition of W used in divertor tiles, for example, are shown to produce undesirable long-lived radionuclides. Finally, waste classifications, based on UK regulations, and a recycling potential limit, have been applied to estimate the time-evolution in waste masses for both the entire vessel (including blanket modules, VV, divertor, and some ex-vessel components) and individual components, and also to suggest when a particular component might be suitable for recycling. The results indicate that the large mass of the VV will not be classifiable as low level waste on the 100-year timescale, but the majority of the divertor will be, and that both components will be potentially recyclable within that time.