Pandemics cause chaotic situations in supply chains (SC) around the globe, which can lead towards survivability challenges. The ongoing COVID-19 pandemic is an unprecedented humanitarian crisis that has severely affected global business dynamics. Similar vulnerabilities have been caused by other outbreaks in the past. In these terms, prevention strategies against propagating disruptions require vigilant goal conceptualization and roadmaps. In this respect, there is a need to explore supply chain operation management strategies to overcome the challenges that emerge due to COVID-19-like situations. Therefore, this review is aimed at exploring such challenges and developing strategies for sustainability, and viability perspectives for SCs, through a structured literature review (SLR) approach. Moreover, this study investigated the impacts of previous epidemic outbreaks on SCs, to identify the research objectives, methodological approaches, and implications for SCs. The study also explored the impacts of epidemic outbreaks on the business environment, in terms of effective resource allocation, supply and demand disruptions, and transportation network optimization, through operations management techniques. Furthermore, this article structured a framework that emphasizes the integration of Industry 4.0 technologies, resilience strategies, and sustainability to overcome SC challenges during pandemics. Finally, future research avenues were identified by including a research agenda for experts and practitioners to develop new pathways to get out of the crisis.