The novel coronavirus infection named COVID-19 was first detected in Wuhan, China, in December 2019, and it has been responsible for significant morbidity and mortality in scores of countries. At the time this article was being written, the number of infected and deceased patients continued to grow worldwide. Most patients with severe forms of the disease suffer from pneumonia and pulmonary insufficiency; in many cases, the disease is generalized and causes multiple organ failures and a dysfunction of physiological systems. One of the most serious and prognostically ominous complications from COVID-19 is coagulopathy, in particular, decompensated hypercoagulability with the risk of developing disseminated intravascular coagulation. In most cases, local and diffuse macro- and microthromboses are present, a condition which causes multiple-organ failure and thromboembolic complications. The causes and pathogenic mechanisms of coagulopathy in COVID-19 remain largely unclear, but they are associated with systemic inflammation, including the so-called cytokine storm. Despite the relatively short period of the ongoing pandemic, laboratory signs of serious hemostatic disorders have been identified and measures for specific prevention and correction of thrombosis have been developed. This review discusses the causes of COVID-19 coagulopathies and the associated complications, as well as possible approaches to their early diagnosis, prevention, and treatment.