Thrombus formation in flowing blood is a complex time- and space-dependent process ofcell adhesion and fibrin gel formation controlled by huge intricate networks ofbiochemical reactions. This combination of complex biochemistry, non-Newtonianhydrodynamics, and transport processes makes thrombosis difficult to understand. That iswhy numerous attempts to use mathematical modeling for this purpose were undertaken duringthe last decade. In particular, recent years witnessed something of a transition from the“systems biology” to the “systems pharmacology/systems medicine” stage: computationalmodeling is being increasingly applied to practical problems such as drug development,investigation of particular events underlying disease, analysis of the mechanism(s) ofdrug’s action, determining an optimal dosing protocols, etc. Here we review recentadvances and challenges in our understanding of thrombus formation.