The disease caused by the coronavirus SARS-CoV-2, named COVID-19, has been spread around the world at a high transmission rate. It was initially considered to be an acute respiratory distress syndrome. Recent clinical data has highlighted that COVID-19 is characterized by a vascular dysfunction and thrombosis, which are not typical for many other acute respiratory diseases. Thrombotic complications are markers of severe COVID-19 and are associated with multiple organ failure and increased mortality. The application of unfractionated and/or low-molecular-weight heparins as anticoagulant medications, significantly reduced the severity of the disease and COVID-19-induced mortality, since heparin is a multifunctional agent. The goal of this review is to summarize the literature data on the pathogenic mechanisms of SARS-CoV-2 and to characterize the properties of heparin, which allow inhibiting these mechanisms at any stage of pathogenesis. We proposed a vicious circle hypothesis of SARS-CoV-2 pathogenesis, as well as an original approach to low-dose heparin therapy beyond its anticoagulant properties. The analysis of a wide range of effects and mechanisms of action of heparin will help create an idea of current possibilities and future potential of applying this drug.