The current legislative framework and the recent energy crisis ask for massive applications of renewable energy sources (RES) in the built environment to reduce energy demand, environmental emissions, and energy costs. The uncritical application of these policies, especially on architectural heritage, could generate serious conservation issues, compromising their heritage values, biodiversity, traditional appearance, and materiality. Thus, there is an urgent call to balance architectural heritage preservation with energy production using clear rules, policies, criteria, and heritage-compatible technologies. The present study aims at defining an updated overview of the application of solar, wind, geothermal energy, and bioenergy on architectural heritage. A deep literature review of the studies published in the years 2020–2023 has been performed, identifying main topics, challenges, advanced solutions, and future perspectives. Acceptability, design criteria, and cutting-edge technologies are also illustrated through case studies to better understand practical approaches.