The residential sector currently accounts for one fifth of global energy use and corresponding greenhouse gas emissions, largely driven by increasing demand for space heating and cooling. Climate change mitigation action requires these to reduce, but the exact decarbonization strategies, the contribution of demand and supply side measures, and their heterogeneity is unclear. Using a regional energy system model with an explicit representation of residential energy use and building stocks, the contribution of this sector in long-term decarbonization pathways is explored. The projections show that in a 2°C scenario, global heating demand is expected to decrease from current levels by 27% and 66% by 2050 and 2100, respectively. However, due to increasing affluence in warmer regions, cooling demand is expected to increase by 176% and 286% respectively. Yet, direct residential emissions are almost eliminated by 2100 by combining increased envelope efficiency and advanced heating technologies in a synergistic manner, where the adoption of high efficiency heating and cooling reduces the need for increased insulation, and vice versa. By combining these measures with rooftop PV, the net energy demand of many household types approaches zero. The exact residential sector strategies vary across local climate, socio-economic, and building stock characteristics.