SARS-CoV-2 is a new beta coronavirus, similar to SARS-CoV-1, that emerged at the end of 2019 in the Hubei province of China. It is responsible for coronavirus disease 2019 (COVID-19), which was declared a pandemic by the World Health Organization on March 11, 2020. The ability to gain quick control of the pandemic has been hampered by a lack of detailed knowledge about SARS-CoV-2-host interactions, mainly in relation to viral biology and host immune response. The rapid clinical course seen in COVID-19 indicates that infection control in asymptomatic patients or patients with mild disease is probably due to the innate immune response, as, considering that SARS-CoV-2 is new to humans, an effective adaptive response would not be expected to occur until approximately 2–3 weeks after contact with the virus. Antiviral innate immunity has humoral components (complement and coagulation-fibrinolysis systems, soluble proteins that recognize glycans on cell surface, interferons, chemokines, and naturally occurring antibodies) and cellular components (natural killer cells and other innate lymphocytes). Failure of this system would pave the way for uncontrolled viral replication in the airways and the mounting of an adaptive immune response, potentially amplified by an inflammatory cascade. Severe COVID-19 appears to be due not only to viral infection but also to a dysregulated immune and inflammatory response. In this paper, the authors review the most recent publications on the immunobiology of SARS-CoV-2, virus interactions with target cells, and host immune responses, and highlight possible associations between deficient innate and acquired immune responses and disease progression and mortality. Immunotherapeutic strategies targeting both the virus and dysfunctional immune responses are also addressed.