PurposeSelecting the optimal supplier is a challenging managerial decision that involves several dimensions that vary over time. Despite the considerable attention devoted to this issue, knowledge is required to be updated and analyzed in this field. This paper reveals new opportunities to advance supplier selection (SS) research from a multidimensional perspective. Moreover, this study aims to formalise SS knowledge to enable the appropriate selection of sustainable, resilient and circular criteria.Design/methodology/approachThis study is developed in two stages: first, a systematic literature review is conducted to select relevant papers. Descriptive and thematic analyses are employed to analyze criteria, solving approaches and case studies. Second, a criterion knowledge-based framework is developed and validated by experts to be implemented as ontology using Protégé software.FindingsEvaluating the viability of suppliers need further studies to integrate other criteria and to align SS objectives with research advancement. Artificial intelligence tools are needed to revolutionize and optimize the traditional techniques used to solve this problem. Literature lucks frameworks for specific sectors. The proposed ontology provides a consistent criteria knowledge base.Practical implicationsFor academics, the results of this study highlight opportunities to improve the viable SS process. From a managerial perspective, the proposed ontology can assist managers in selecting the appropriate criteria. Future works can enrich the proposed ontology and integrate this knowledge base into an information system.Originality/valueThis study contributes to promoting knowledge about viable SS. Capitalizing the knowledge base of criteria in a computer-interpretable manner supports the digitalization of this critical decision.