The coronavirus disease 2019 (COVID-19), a deadly pandemic that has affected millions of people worldwide, is associated with cardiovascular complications, including venous and arterial thromboembolic events. Viral spike proteins, in fact, may promote the release of prothrombotic and inflammatory mediators. Vaccines, coding for the spike protein, are the primary means for preventing COVID-19. However, some unexpected thrombotic events at unusual sites, most frequently located in the cerebral venous sinus but also splanchnic, with associated thrombocytopenia, have emerged in subjects who received adenovirus-based vaccines, especially in fertile women. This clinical entity was soon recognized as a new syndrome, named vaccine-induced immune thrombotic thrombocytopenia, probably caused by cross-reacting anti-platelet factor-4 antibodies activating platelets. For this reason, the regulatory agencies of various countries restricted the use of adenovirus-based vaccines to some age groups. The prevailing opinion of most experts, however, is that the risk of developing COVID-19, including thrombotic complications, clearly outweighs this potential risk. This point-of-view aims at providing a narrative review of epidemiological issues, clinical data, and pathogenetic hypotheses of thrombosis linked to both COVID-19 and its vaccines, helping medical practitioners to offer up-to-date and evidence-based counseling to their often-alarmed patients with acute or chronic cardiovascular thrombotic events.