Blood coagulation at the place of the complete severing of a vessel or puncturing of a vessel sidewall is usually a beneficial reaction, as it protects the body from bleeding and maintains hemostasis, while the formation of a blood clot inside the blood vessel is a pathological phenomenon, which is highly dangerous, and sometimes leads to serious complications. In this paper, two scales of modelling blood thrombosis will be introduced using numerical methods and fluid dynamics. The meso-scale model of the flow is described by Navier-Stokes equations and the blood thrombosis model is based on equations of transport and diffusion. The equations describing levels of concentrations of factors responsible for blood coagulation can be implemented into a solver solving Navier-Stokes equations, what will enable simulation of blood flow and estimation of the risk of thrombus formation related to flow conditions. The proposed micro-scale model is using molecular dynamics to simulate interactions between blood cells and vascular walls. An effective combination of both models is possible thanks to the introduction of the multiple-time stepping algorithm, which enables a full visualization of blood flow, coupling molecular interaction with the fluid mechanics equation. The goal of the paper is to present the latest literature review on the possibilities of blood coagulation modelling in two scales and the main achievements in blood thrombosis research: the key role of transport and experimental background.