Blood is a bodily fluid that is vital for a number of life functions in animals. To a first approximation, blood is a mildly alkaline aqueous fluid (plasma) in which a large number of free-floating red cells (erythrocytes), white cells (leucocytes), and platelets are suspended. The primary function of blood is to transport oxygen from the lungs to all the cells of the body and move carbon dioxide in the return direction after it is produced by the cells’ metabolism. Blood also carries nutrients to the cells and brings waste products to the liver and kidneys. Measured levels of oxygen, nutrients, waste, and electrolytes in blood are often used for clinical assessment of human health. Raman spectroscopy is a non-destructive analytical technique that uses the inelastic scattering of light to provide information on chemical composition, and hence has a potential role in this clinical assessment process. Raman spectroscopic probing of blood components and of whole blood has been on-going for more than four decades and has proven useful in applications ranging from the understanding of hemoglobin oxygenation, to the discrimination of cancerous cells from healthy lymphocytes, and the forensic investigation of crime scenes. In this paper, we review the literature in the field, collate the published Raman spectroscopy studies of erythrocytes, leucocytes, platelets, plasma, and whole blood, and attempt to draw general conclusions on the state of the field.