Buildings account for 36% of global final energy demand and are key to mitigating climate change. Assessing the evolution of the global building stock and its energy demand is critical to support mitigation strategies. However, most global studies lack granularity and overlook heterogeneity in the building sector, limiting the evaluation of demand transformation scenarios. We develop global residential building scenarios along the shared socio-economic pathways (SSPs) 1–3 and assess the evolution of building stock, energy demand, and CO2 emissions for space heating and cooling with MESSAGEix-Buildings, a modelling framework soft-linked to an integrated assessment framework. MESSAGEix-Buildings combines bottom-up modelling of energy demand, stock turnover, and discrete choice modelling for energy efficiency decisions, and accounts for heterogeneity in geographical contexts, socio-economics, and buildings characteristics.