The novel coronavirus named severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has generated the ongoing coronavirus disease-2019 (COVID-19) pandemic, still with an uncertain outcome. Besides pneumonia and acute lung injury (ALI) or acute respiratory distress syndrome (ARDS), other features became evident in the context of COVID-19. These includes endothelial and coagulation dysfunction with disseminated intravascular coagulation (DIC), and multiple organ dysfunction syndrome (MODS), along with the occurrence of neurological alterations. The multi-system nature of such viral infection is a witness to the exploitation and impairment of ubiquitous subcellular and metabolic pathways for the sake of its life-cycle, ranging from host cell invasion, replication, transmission, up to a cytopathic effect and overt systemic inflammation. In this frame, alterations in cell-clearing systems of the host are emerging as a hallmark in the pathogenesis of various respiratory viruses, including SARS-CoV-2. Indeed, exploitation of the autophagy and proteasome pathways might contribute not only to the replication of the virus at the site of infection but also to the spreading of either mature virions or inflammatory mediators at both cellular and multisystem levels. In this frame, besides a pharmacological therapy, many researchers are wondering if some non-pharmacological substances might counteract or positively modulate the course of the infection. The pharmacological properties of natural compounds have gained increasing attention in the field of alternative and adjunct therapeutic approaches to several diseases. In particular, several naturally-occurring herbal compounds (mostly polyphenols) are reported to produce widespread antiviral, anti-inflammatory, and anti-oxidant effects while acting as autophagy and (immuno)-proteasome modulators. This article attempts to bridge the perturbation of autophagy and proteasome pathways with the potentially beneficial effects of specific phytochemicals and flavonoids in viral infections, with a focus on the multisystem SARS-CoV-2 infection.