PurposeCorporate sustainability (CS) is becoming a popular research topic. In recent years, researchers have conducted a significant number of studies in this area. Although a number of those studies have used a variety of multicriteria decision-making (MCDM) methods, to date there is no systematic literature review of this area of research. This paper fulfills this research gap.Design/methodology/approachThe authors use a systematic literature review and bibliometric analysis approach to analyze the applications of MCDM methods in research on CS.FindingsThe authors have observed that both single and integrated MCDM methods have been used in this domain; however, single MCDM methods are dominant. Further, this review shows that most of the integrated methods use only two MCDM methods and that there has been no comparison of results obtained from different MCDM methods. After reviewing these developments and summarizing the findings, the authors propose directions for future research, including investigating and formulating strategies for specific CS initiatives, integrating three or more MCDM methods, integrating MCDM methods with optimization techniques, analyzing results from a small and medium-sized enterprise (SME) perspective, reconsidering the tenets of existing theories via MCDM methods, and comparing the results of studies of CS in different kinds of economies, as well as the results of using different MCDM methods.Originality/valueTo the best of the authors' knowledge, this is the first study that has conducted a systematic literature review to analyze applications of MCDM methods to different aspects of corporate sustainability, including enablers of and barriers to CS, the evaluation and design of CS initiatives, system or strategy formulation, and performance evaluation, among others.