In order to contribute to the German Energiewende (energy transition) adequately, the building sector has to be almost completely decarbonised in the long term. Our analysis investigates how the German building stock can be transformed into a nearly climate-neutral state by 2050. Using a stock modelling approach based on a typology of the German residential and non-residential building sector, we develop different visions (target states) of what a nearly climate-neutral building stock could look like. All developed target states achieve the overall goal of reducing the non-renewable primary energy demand in 2050 by at least 80%. In order to span a broad target corridor, the target states differ in the two central target dimensions: efficiency (reduction in final energy demand) and energy/technology supply mix (especially the herein contained share of renewable energies). Additionally, using the energy system model REMod-D, the interactions of the building stock with the energy system as a whole are investigated. We explore the differences between a target state focussing on efficiency measures and a target state where efficiency is partly compensated for by an increased use of renewable energies. We learn that from a private cost perspective no clear recommendation can be derived as to which target state should be given priority. This means that other criteria become more relevant, such as social acceptance regarding the different measures, or the challenges that arise from rolling out additional renewable energy capacity on top of what is necessary to achieve the climate goals in other sectors.