The novel coronavirus disease 2019 has rapidly increased in pandemic scale since it first appeared in Wuhan, China, in December 2019. In these troubled days the scientific community is asking for rapid replies to prevent and combat the emergency. It is generally accepted that only achieving a better understanding of the interactions between the virus and the host immune response and of the pathogenesis of infection is crucial to identify valid therapeutic tools to control virus entry, replication, and spread as well as to impair its lethal effects. On the basis of recent research progress of severe acute respiratory syndrome coronavirus 2 and the results on previous coronaviruses, in this contribution we underscore some of the main unsolved problems, mostly focusing on pathogenetic aspects and host immunity to the virus. On this basis, we also touch important aspects regarding the immune response in asymptomatic subjects, the immune evasion of severe acute respiratory syndrome coronavirus 2 in severe patients, and differences in disease severity by age and sex.