This article provides a critical review of the literature on the relationship between renewable energies and sustainability considering the three dimensions of sustainability: economic, social, and environmental. First, a bibliometric tool is used and then a more in-depth analysis of selected literature is performed, focusing on the type of renewable energy analyzed and the level of development of countries, the dimension of sustainability focused on and the country’s development level, and the type of renewable energies focused on and the dimension of sustainability analyzed. It represents a milestone in the topic giving insights on the state of the art of the research on this research area, enhancing empirical evidence on the kind of relationships and developing a discussion on how closely aligned the political and institutional discourses are with the research concerns. We conclude that, while studies on lower-income countries focus on lower-rung energies, studies on higher-income countries focus on the study of more diversified sources. Moreover, wind–solar energy is the most reported in the articles concerned with environmental sustainability. Our main recommendation is to further investigate the implementation of modern renewable energies in developing countries, to help those countries to climb the energy ladder toward cleaner energy supply.