SARS-CoV-2 is a new type of coronavirus that has caused worldwide pandemic. The disease induced by SARS-CoV-2 is called COVID-19. A majority of people with COVID-19 have relatively mild respiratory symptoms. However, a small percentage of COVID-19 patients develop a severe disease where multiple organs are affected. These severe forms of SARS-CoV-2 infections are associated with excessive production of pro-inflammatory cytokines, so called “cytokine storm”. Inflammasomes, which are protein complexes of the innate immune system orchestrate development of local and systemic inflammation during virus infection. Recent data suggest involvement of inflammasomes in severe COVID-19. Activation of inflammasome exerts two major effects: it activates caspase-1-mediated processing and secretion of pro-inflammatory cytokines IL-1β and IL-18, and induces inflammatory cell death, pyroptosis, via protein called gasdermin D. Here, we provide comprehensive review of current understanding of the activation and possible functions of different inflammasome structures during SARS-CoV-2 infection and compare that to response caused by influenza A virus. We also discuss how novel SARS-CoV-2 mRNA vaccines activate innate immune response, which is a prerequisite for the activation of protective adaptive immune response.