The relevant literature on the intensity of anticoagulation needed to prevent the development or growth of thrombi in patients at risk is reviewed. In case of elective surgery, prevention of venous thrombosis is easily attained with heparin or with coumarin alone, at levels of anticoagulation involving only a minor risk of bleeding complications. For posttraumatic prophylaxis, more intensive oral anticoagulation is required, similar to that for the management of active venous thrombosis, for which a combined heparin/coumarin regimen is proposed. A 90% reduction of the incidence of systemic emboli in patients with a high risk of developing intracardiac thrombosis requires high-intensity treatment with a target INR of 4. More intensive anticoagulation would be needed to obtain the same 90% protection in case of arterial (coronary) thrombosis. This is prohibited, however, by the rapidly increasing bleeding risk in cases with INR values greater than 5. With a target INR of 3.5 (sixty-Plus patients), the reinfarction rate will not be lowered by more than two thirds. Antiplatelet drugs given alone or in combination with anticoagulants have not been convincingly successful thus far in the prevention and treatment of thrombosis.