As the world faces the current SARS-CoV-2 pandemic, extensive efforts have been applied to identify effective therapeutic agents. Convalescent plasma collected from recovered patients has been a therapeutic modality employed for over a hundred years for various infectious pathogens. Specifically, it has been used in the treatment of many viral infections with varying degrees of clinical efficacy. As we consider the use of convalescent plasma in the battle against this new strain of coronavirus, it is prudent to review what is known from past experiences. Accordingly, the aim of this review is to examine in detail studies of convalescent plasma used during previous viral outbreaks and pandemics with particular focus on hemorrhagic fevers, influenza, and other coronaviruses. The concluding sections of this review address the potential use of convalescent plasma during the present-day SARS-CoV-2 pandemic, not only insofar as its clinical benefit but also the steps required to make convalescent plasma treatments readily available for an exponentially growing patient population. By the end, the authors hope to address the extent to which convalescent plasma represents a realistic therapeutic approach, or a distraction from other potentially useful treatments.