Energy poverty is one of the main challenges facing humanity in the 21st century. Research on energy poverty is becoming a common focus of scholars in many areas. Bibliometrics can help researchers dig deep into the information of specific research fields from a quantitative perspective. In this study, we collected 1018 research papers in the field of energy poverty published in the period 1999–2019 from the Web of Science databases and conducted a bibliometric analysis on them. Cleaning and screening of sample papers, matrix construction, and visualization were performed using Bibliometrix, VOSviewer, and HistCite, summarizing the internal and external characteristics of the papers. With regard to external characteristics, a total of 982 research institutions in 80 regions conducted research in this field. There is extensive cooperation between the countries, and the UK, the USA, Australia, and Italy play the most active role in the cooperation network. With regard to internal characteristics, we found the two most representative citation paths: one path starts from the concerns of energy-poor groups and stops at an ethical discussion on energy poverty; the second path is based on the existing technological path, continuously developing coping policies, evaluation methods, and a conceptual framework for dealing with energy poverty. Furthermore, through coupling analysis, we discovered four focuses of energy poverty research: improvement of definition, improvement of evaluation methods, effects of coping policy, and energy justice. Through a comprehensive analysis of existing papers, this paper reveals some limitations of previous studies and recommends some promising directions for future research on energy poverty.