Hemostasis is the physiological process of maintaining blood circulation in the event of a breach in integrity of vessel wall (like in trauma) by initially forming a localized clot to contain blood loss, restricting the clot to the site of breach only and later actively dissolving the clot as a part of repair to restore normal circulation through the affected vessels. Hemostasis, thus, is one of the most finely balanced physiological process involving coagulation when required followed by appropriately timed lysis of the clot formed. This chapter covers the physiology of hemostatsis, plasma factors regulating coagulation, cyclooxygenase, NSAIDs, cardiovascular safety and platelet inhibition, and thrombosis. Cooxygenase (COX) catalyzes the conversion of arachidonic acid into prostaglandin H2 and further into prostanoids by actions of isomerase. Platelets contain only COX-1, and its inhibition would block thromboxane A2 (Tx2) production and result in suppressing platelets aggregation and local vasoconstriction.