Aspects of mechanical deformability and biorheology of the human red blood cell are known to play a pivotal role in influencing organ function as well as states of overall health and disease. In this article, consequences of alterations to the membrane and cytoskeletal molecular structure of the human red blood cell are considered in the context of an infectious disease, Plasmodium falciparum malaria, and several hereditary hemolytic disorders: spherocytosis, elliptocytosis, and sickle cell anemia. In each of these cases, the effects of altered cell shape or molecular structure on cell elasticity, motility, and biorheology are examined. These examples are used to gain broad perspectives on the connections among cell and subcellular structure, properties, and disease at the intersections of engineering, biology, and medicine.