Blood is a complex fluid whose behavior under flow is poorly understood. A constitutive model accurately representing the rheology of blood unquestionably misses to describe the many situations where blood flows, both in the physiological and industrial contexts. Hemorheology is actually in its infancy as blood has mainly been studied by physiologists so far, who do not have the skills to perform the quantitative analysis necessary to construct such a model. Blood complexity comes from its multiphase nature: it is a dense suspension of aggregable and deformable particles. Developing a constitutive model for blood is thus a scientific challenge that can only be tackled with the support of new experimental and numerical data as well as the joint expertise of a multidisciplinary team. By providing Montpellier with a numerical and material platform dedicated to the study of blood rheophysics, RheoBlood will federate 11 academic, industrial and clinical groups with the ambition to take up the challenge of developing a constitutive model for blood. This scientific project goes hand in hand with a strategy aiming at making Montpellier a major site for the knowledge of blood flows, in terms of research, formation and technology transfer to the industry and the clinical practice.