Therapeutic red blood cell (RBC) transfusion is widely utilized in the management of anaemia. Critically ill intensive care unit (ICU) patients in particular, as well as medical and haematology–oncology patients, are among the largest groups of users of RBC products. While anaemia is common in these patients, its treatment and management, including appropriate thresholds for RBC transfusion, remain controversial. We review here the function of RBCs in oxygen transport and physiology, with a view to their role in supporting and maintaining systemic tissue oxygenation. Adaptive and physiological compensatory mechanisms in the setting of anaemia are discussed, along with the limits of compensation. Finally, data from clinical studies will be examined in search of evidence for, or against, a clinically relevant transfusion trigger.