Anticoagulant drugs have been used to prevent and treat thrombosis. However, they are associated with risk of hemorrhage. Therefore, prior to their clinical use, it is important to assess the risk of bleeding and thrombosis. In case of older anticoagulant drugs like heparin and warfarin, dose adjustment is required owing to narrow therapeutic ranges. The established monitoring methods for heparin and warfarin are activated partial thromboplastin time (APTT)/anti-Xa assay and prothrombin time – international normalized ratio (PT-INR), respectively. Since 2008, new generation anticoagulant drugs, called direct oral anticoagulants (DOACs), have been widely prescribed to prevent and treat several thromboembolic diseases. Although the use of DOACs without routine monitoring and frequent dose adjustment has been shown to be safe and effective, there may be clinical circumstances in specific patients when measurement of the anticoagulant effects of DOACs is required. Recently, anticoagulation therapy has received attention when treating patients with coronavirus disease 2019 (COVID-19). In this review, we discuss the mechanisms of anticoagulant drugs—heparin, warfarin, and DOACs and describe the methods used for the measurement of their effects. In addition, we discuss the latest findings on thrombosis mechanism in patients with COVID-19 with respect to biological chemistry.