We present a concise summary of mathematical models for the formation and dissolution of blood clots (in other words for the process of hemostasis). For lack of space we restrict our attention to very few models, selected from a very large literature, trying to emphasize the variety of methods and viewpoints. A peculiar aspect concerning hemostasis is the fact that a new interpretation of its extremely complex biological mechanism has been found rather recently, so that most of the mathematical models should be revisited. Also in view of this fact we believed that it was absolutely necessary to write an extensive introduction to the various aspects of hemostasis, including some history, and not disregarding a description of bleeding disorders (another large field of investigation for mathematical modelling), from which much has been learned about the role and importance of each of the numerous elements intervening in hemostasis. We realize that our work is necessarily incomplete. Indeed, our conclusion is that mathematicians are still in front of the huge task of keeping up with the developments of the medical theory and of the therapeutical practice of this multifaceted subject.