In addition to immunological and wound healing cell and platelet delivery, ion stasis and nutrient supply, blood delivers oxygen to cells and tissues and removes metabolic wastes. For decades researchers have been trying to develop approaches that mimic these two immediately vital functions of blood. Oxygen is crucial for the long-term survival of tissues and cells in vertebrates. Hypoxia (oxygen deficiency) and even at times anoxia (absence of oxygen) can occur during organ preservation, organ and cell transplantation, wound healing, in tumors and engineering of tissues. Different approaches have been developed to deliver oxygen to tissues and cells, including hyperbaric oxygen therapy (HBOT), normobaric hyperoxia therapy (NBOT), using biochemical reactions and electrolysis, employing liquids with high oxygen solubility, administering hemoglobin, myoglobin and red blood cells (RBCs), introducing oxygen-generating agents, using oxygen-carrying microparticles, persufflation, and peritoneal oxygenation. Metabolic waste accumulation is another issue in biological systems when blood flow is insufficient. Metabolic wastes change the microenvironment of cells and tissues, influence the metabolic activities of cells, and ultimately cause cell death. This review examines advances in blood mimicking systems in the field of biomedical engineering in terms of oxygen delivery and metabolic waste removal.