The challenges of global economies foster supply chains to have to increase their processes of collaboration and dependence between their nodes, generating an increase in the level of vulnerability to possible impacts and interruptions in their operations that may affect their sustainability. This has developed an emerging area of interest in supply chain management, considering resilience management as a strategic capability of companies, and causing an increase in this area of research. Additionally, supply chains should deal with the three dimensions of sustainability (economic, environmental, and social dimensions) by incorporating the three types of objectives in their strategy. Thus, there is a need to integrate both resilience and sustainability in supply chain management to increase competitiveness. In this paper, a systematic literature review is undertaken to analyze resilience management and its connection to increase supply chain sustainability. In the review, 232 articles published from 2000 to February 2020 in peer-reviewed journals in the Scopus and ScienceDirect databases are analyzed, classified, and synthesized. With the results, this paper develops a conceptual framework that integrates the fundamental elements for analyzing, measuring, and managing resilience to increase sustainability in the supply chain. Finally, conclusions, limitations, and future research lines are exposed.