Devastating pandemics, such as that due to COVID-19, can provide strong testimony to our knowledge of the genetic and evolutionary determinants of infectious disease susceptibility and severity. One of the most remarkable aspects of such outbreaks is the stunning interindividual variability observed in the course of infection. In recent decades, enormous progress has been made in the field of the human genetics of infectious diseases, and an increasing number of human genetic factors have been reported to explain, to a great extent, the observed variability for a large number of infectious agents. However, our understanding of the cellular, molecular, and immunological mechanisms underlying such disparities between individuals and ethnic groups, remains very limited. Here, we discuss recent findings relating to human genetic predisposition to infectious disease, from an immunological or population genetic perspective, and show how these and other innovative approaches have been applied to deciphering the genetic basis of human susceptibility to COVID-19 and the severity of this disease. From an evolutionary perspective, we show how past demographic and selection events characterizing the history of our species, including admixture with archaic humans, such as Neanderthals, facilitated modern human adaptation to the threats imposed by ancient pathogens. In the context of emerging infectious diseases, these past episodes of genetic adaptation may contribute to some of the observed population differences in the outcome of SARS-CoV-2 infection and the severity of COVID-19 illness.