The COVID-19 pandemic unveils unforeseen and unprecedented fragilities of the supply chains (SC). One strong stressor to SCs and their numerous collapses comes from disruption propagations through the networks. The existing knowledge in modelling disruption propagations in SCs is multi-faceted and deserves to be analysed for the unique set of factors shaping SC adaptations during and after a global pandemic. We scrutinize OR studies published in international journals and dealing with disruption propagation in SCs. This streamlining of the literature allowed revealing several new research tensions and novel categorizations/classifications. Our study pursues two major contributions subject to two research questions. First, we collate the state-of-the-art in research on disruption propagations in SCs and identify a methodical taxonomy and theories displaying the value and applications of OR methods to coping with pandemic impacts on the SCs. Second, we reveal and systemize managerial insights from the theory that can be used for operating (adapting) amid a pandemic and at the times of recovery along with withstanding future pandemics. In particular, we find that outcomes of the OR contributions and the resulting managerial insights can be categorized into three levels, i.e., network, process, and control. Our outcomes in both managerial and theoretical domains are structured into five stages (i.e., Anticipation; Early detection; Containment; Control and Mitigation; and Elimination) following the WHO classification. Our study can be used by industry and researchers alike in order to progress the decision-support systems guiding the SCs amid the COVID-19 pandemic and recovering them thereafter. Suggestions for future research directions are offered and discussed.