Cells actively interact with their microenvironment, constantly sensing and modulating biochemical and biophysical signals. Blood comprises a variety of non-adherent cells that interact with each other and with endothelial and vascular smooth muscle cells of the blood vessel walls. Blood cells are further experiencing a range of external forces by the hemodynamic environment and they also exert forces to remodel their local environment. Therefore, the biophysics and material properties of blood cells and blood play an important role in determining blood behaviour in health and disease. In this Review, we discuss blood cells and tissues from a materials perspective, considering the mechanical properties and biophysics of individual blood cells and endothelial cells as well as blood cell collectives. We highlight how blood vessels provide a mechanosensitive barrier between blood and tissues and how changes in vessel stiffness and flow shear stress can be correlated to plaque formation and exploited for the design of vascular grafts. We discuss the effect of the properties of fibrin on blood clotting, and investigate how forces exerted by platelets are correlated to disease. Finally, we hypothesize that blood and vascular cells are constantly establishing a mechanical homeostasis, which, when imbalanced, can lead to hematologic and vascular diseases.