The clinical manifestations of coronavirus disease (COVID-19) are highly variable, ranging from asymptomatic cases to life-threatening complications and death. Severe disease progression is more common in older individuals and males, as well as in the presence of various comorbidities. Beyond these risk factors, the intrinsic characteristics of the virus and the host genetic factors also contribute to the heterogeneous clinical course of COVID-19. Genetic research is fundamental in understanding the biological mechanisms underlying congenital diseases, identifying the genes and proteins responsible for the susceptibility to various inherited conditions, recognizing therapeutically relevant targets, suggesting drug repurposing, and clarifying causal relationships for modifiable environmental risk factors. Although these studies typically take a long time to conduct, especially to translate their findings into clinical practice, the scientific community has swiftly uncovered genetic signals underlying the diverse COVID-19 phenotypes. In this review, in addition to a concise summary of SARS-CoV-2 recognition and the initial steps of the immune responses, we aim to provide an overview of the literature concerning the genetic factors associated with susceptibility to the disease and its severe progression. We also review the pioneering research in identifying the affected genes and the most significant genome-wide association studies, covering both common and rare genetic variants, which have greatly contributed to understand the etiology of the disease and have guided effective COVID-19 treatment during the most challenging times.