The continued pressure of COVID-19 on public health worldwide underlines the need for a better understanding of the mechanisms of disease caused by severe acute respiratory syndrome coronavirus-2. Though many animal models are readily available for use, the nonhuman primate (NHP) models are considered the gold standard in recapitulating disease progression in humans. In this review, we highlight the relevant research since the beginning of the pandemic to critically evaluate the importance of this model. We characterize the disease’s clinical manifestations, aspects of viral replication and shedding, induction of the host’s immune response, and pathological findings that broaden our understanding of the importance of NHPs in research to strengthen our public health approach to the pandemic.