The hematological effects of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are important in COVID-19 pathophysiology. However, the interactions of SARS-CoV-2 with platelets and red blood cells are still poorly understood. There are conflicting data regarding the mechanisms and significance of these interactions. The aim of this review is to put together available data and discuss hypotheses, the known and suspected effects of the virus on these blood cells, their pathophysiological and diagnostic significance, and the potential role of platelets and red blood cells in the virus’s transport, propagation, and clearance by the immune system. We pay particular attention to the mutual activation of platelets, the immune system, the endothelium, and blood coagulation and how this changes with the evolution of SARS-CoV-2. There is now convincing evidence that platelets, along with platelet and erythroid precursors (but not mature erythrocytes), are frequently infected by SARS-CoV-2 and functionally changed. The mechanisms of infection of these cells and their role are not yet entirely clear. Still, the changes in platelets and red blood cells in COVID-19 are significantly associated with disease severity and are likely to have prognostic and pathophysiological significance in the development of thrombotic and pulmonary complications.