Many natural coumarins and their chemically synthesized analogs and derivatives exert diverse properties, such as anticancer, antioxidant, anti-inflammatory, or anticoagulant, with the latter being of the utmost importance. The widely used warfarin, acenocoumarol, and phenprocoumon exert anticoagulant properties by inhibiting the vitamin K epoxide reductase complex. In this interdisciplinary review, we present biochemical principles of the coagulation processes and possible methods for their tuning based on the use of coumarins. We also summarize chemical methods of synthesis of coumarins and discuss structures and properties of those that have been used for a long time, as well as newly synthesized compounds. Brief information on the clinical use of coumarins and other anticoagulant drugs is given, including the severe effects of overdosing and methods for reversing their action.