One of the most dangerous features of the new coronavirus infection caused by the SARS-CoV-2 virus is the tendency of the hemostasis system of patients to excessive thrombus formation. Among the possible causes of this pathology, both the activation of vascular endothelial cells, leading to the exposure of tissue factor by these cells, and direct activation of the plasma hemostasis were named. Besides, there is a significant change in platelet responses to activation, which is not accompanied by significant thrombocytopenia. The mechanism of platelet dysfunction is rather controversial. On the one hand, there are suggestions that platelets can act as a direct “container” for the virus, thus spreading it throughout the body. On the other hand, the presence of viral RNA in platelets has been demonstrated in only one study, while other authors have obtained the opposite result. Another mechanism of the virus's direct effect on platelets is the penetration of the virus into megakaryocytes and the subsequent violation of thrombocytopoiesis. However, three of the four published works show that platelets from patients with SARS-CoV-2 are in an activated state (the so-called platelet pre-activation). This phenomenon can be caused by the direct influence of the virus and the effect of thromboinflammation in the lungs on platelet functions. Here we review the known data and possible causes of the platelet functionality changes observed in patients with SARS-CoV-2.