Since its adoption in September 2015, the 2030 Agenda has laid the foundations for a model of shared prosperity for a sustainable world. The current global pandemic highlights profound inequalities affecting our economies, health, and quality of life. For this reason, the aim of this study was to present the current state of scientific research related to inequality, poverty, and climate change, and to propose lines of improvement that can contribute to achieving three of the 17 SDGs (end poverty, SDG 1; reduce inequality, SDG 10; and climate action, SDG 13), proposed in the 2030 Agenda. For this purpose, we undertook a systematic literature review. The results show that the subject of poverty, inequality, and climate change has been little studied or articulated by researchers, and significant differences exist between the different areas studied. The highest number of publications (51.7%) is associated with topics related to sustainability—environment and economics. The remainder are distributed among 12 other research areas. Another relevant finding is that the effects of climate change are more pressing for more vulnerable populations, including impoverished women from rural areas and children from underdeveloped countries. This gender and social inequality has been rarely addressed in studies. Food security and energy poverty is another under-researched area. According to the results obtained in this work, we consider that the circular economy may improve these indicators, constituting a line of future research. Thus, one of the main objectives of this approach is to eliminate negative externalities, specifically the existing social inequalities within the current linear economy model.