Sustainable supplier selection (SSS) is an essential part of the decision-making process in sustainable supply chains. Numerous research studies have been conducted using various decision-making methods to attend to this research-worthy issue. This literature review presents a comprehensive SSS analysis focusing on social, economic, and environmental aspects. The present study spans five years (2018–2022) and considers 101 papers. It provides a detailed breakdown of the papers based on their dates of publication, the countries of the writers, application fields, and journals, and it categorizes them based on their approaches. In addition, this review examines the use of single- or hybrid-form methodologies in the papers reviewed. It also identifies that the TOPSIS, AHP, VIKOR, BWM, DEA, DEMATEL, and MULTIMOORA methods and their extensions are the most frequently used methods in SSS studies. It is concluded that hybrid approaches and their rough, grey, and fuzzy extensions are used to solve real-world problems. However, state-of-the-art mathematical tools, such as soft sets and their hybrid versions with fuzzy sets, have not been utilized in SSS studies. Therefore, this study inspires and encourages the use of such tools in SSS research.