Public acceptability of energy sources and mitigation technologies is critical for a successful energy transition worldwide, which is related to their perceived impacts. This review extends previous work by synthesising peer-reviewed literature on public evaluations of eleven key energy sources and mitigation technologies central to the energy transition: biomass, carbon capture and storage (CCS), coal, energy storage technologies, geothermal energy, hydroelectric energy, natural gas, nuclear power, oil, solar, and wind power. We analysed 141 qualitative and quantitative articles published between January 2000 and May 2021. Acceptability was highest for solar, hydroelectric, and wind power, moderate for biomass, natural gas, nuclear energy, and CCS, and lowest for oil and coal. Insufficient evidence was available of acceptability of geothermal energy and energy storage. Acceptability was typically lower for local project implementation than for general-level evaluations of biomass, CCS, natural gas, and wind energy, while the opposite was true for nuclear energy. We identified six categories of perceived impacts: aesthetic, economic, environmental, community and health, temporal, and usability. Economic, environmental, and community and health impacts of energy sources and mitigation technologies were most frequently studied. Renewable energy sources—wind, solar, and hydroelectric power—were perceived more positively than fossil fuels, nuclear energy, and CCS, particularly regarding environmental and community and health impacts. Our findings suggest broad public support for transitioning from fossil fuels to low-carbon technologies, though local projects may face greater opposition.