An interesting problem in hemorheology is to calculate that volume fraction of erythrocytes (hematocrit) that is optimal for transporting a maximum amount of oxygen. If the hematocrit is too low, too few erythrocytes are present to transport oxygen. If it is too high, the blood is very viscous and cannot flow quickly, so that oxygen supply to the tissues is again reduced. These considerations are very important, since oxygen transport is an important factor for physical performance. Here, we derive theoretical optimal values of hematocrit in vertebrates and collect, from the literature, experimentally observed values for 57 animal species. It is an interesting question whether optimal hematocrit theory allows one to calculate hematocrit values that are in agreement with the observed values in various vertebrate species. For this, we first briefly review previous approaches in that theory. Then we check which empirical or theoretically derived formulas describing the dependence of viscosity on concentration in a suspension lead to the best agreement between the theoretical and observed values. We consider both spatially homogeneous and heterogeneous distributions of erythrocytes in the blood and also possible extensions, like the influence of defective erythrocytes and cases where some substances are transported in the plasma. By discussing the results, we critically assess the power and limitations of optimal hematocrit theory. One of our goals is to provide a systematic overview of different approaches in optimal hematocrit theory.