Interaction among individuals is universal, both in animals and in plants, and substantially affects evolution of natural populations and responses to artificial selection in agriculture. Although quantitative genetics has successfully been applied to many traits, it does not provide a general theory accounting for interaction among individuals and selection acting on multiple levels. Consequently, current quantitative genetic theory fails to explain why some traits do not respond to selection among individuals, but respond greatly to selection among groups. Understanding the full impacts of heritable interactions on the outcomes of selection requires a quantitative genetic framework including all levels of selection and relatedness. Here we present such a framework and provide expressions for the response to selection. Results show that interaction among individuals may create substantial heritable variation, which is hidden to classical analyses. Selection acting on higher levels of organization captures this hidden variation and therefore always yields positive response, whereas individual selection may yield response in the opposite direction. Our work provides testable predictions of response to multilevel selection and reduces to classical theory in the absence of interaction. Statistical methodology provided elsewhere enables empirical application of our work to both natural and domestic populations.