A flexible coupling of power and heat sectors can contribute to both renewable energy integration and decarbonization. We present a literature review of model-based analyses in this field, focusing on residential heating. We compare geographical and temporal research scopes and identify state-of-the-art analytical model formulations, particularly considering heat pumps and thermal storage. While numerical findings are idiosyncratic to specific assumptions, a synthesis of results indicates that power-to-heat technologies can cost-effectively contribute to fossil fuel substitution, renewable integration, and decarbonization. Heat pumps and passive thermal storage emerge as particularly favorable options.