The function of blood is to feed all the tissues of the body with vital materials and to remove waste. To do this in the human adult it has to traverse the complicated vascular network, which varies in diameter from some 3 cm down to about 5 μm. Furthermore, the blood must circulate above a limiting rate if it is to do its work effectively enough to keep the organism healthy. This rate of circulation is determined by the driving pressure generated by the heart, by the geometrical resistance offered by the vasculature and by the flow properties of the blood. These flow properties are the concern of the hemorheologist and they are dependent on the composition of the blood and the properties of its constituents; hence, knowledge of them is vital to any understanding of hemorheology. This chapter gives an overview of the composition of normal adult human blood and some indication of the ways in which it can be altered in diseased states. There is also discussion of the normal changes in blood composition that take place as the fetus develops through to the neonatal period. Finally, there is a brief review of the variations that occur in other mammals, emphasizing the similarities and the great differences that exist compared with the human adult.