Abstract Buildings energy consumption is one of the most important contributors to greenhouse gas (GHG) emissions worldwide, responsible for 23% of energy-related CO2 emissions. Decarbonising the energy demand of buildings will require two types of strategies: first, an overall reduction in energy demand, which could, to some extent, be achieved at negative costs; and second through a reduction of the carbon content of energy via fuel switching and supply-side decarbonisation. This study assesses the contributions of each of these strategies for the decarbonisation of the buildings sector in line with a 1.5°C global warming. We show that in a 1.5°C scenario combining mitigation policies and a reduction of market failures in efficiency markets, 81% of the reductions in buildings emissions are achieved through the reduction of the carbon content of energy, while the remaining 19% are due to efficiency improvements which reduce energy demand by 31%. Without supply-side decarbonisation, efficiency improvements almost entirely suppress the doubling of emissions that would otherwise be expected, but fail to induce an absolute decline in emissions. Our modelling and scenarios show the impact of both climate change mitigation policies and of the alleviation of market failures pervading through energy efficiency markets. The results show that the reduction of the carbon content of energy through fuel switching and supply-side decarbonisation is of paramount importance for the decarbonisation of buildings.