The rheology of artificial blood studies the properties of flow and the deformation of blood substitutes designed to imitate the behavior of natural blood. These synthetic fluids must reproduce essential characteristics such as non-Newtonian viscosity, thixotropy, and elasticity, in order to ensure efficient oxygen transport and optimal interaction with biomedical devices. The understanding of the rheological mechanisms allows to improve the formulation of artificial blood for clinical applications, notably in transfusion, in extracorporeal circulation, or in biomedical research. What domains combine experimental approaches and numerical modeling to optimize functional performances and biocompatibility of products.