This chapter makes the first attempt to quantify the amount of discriminatory information in finger vein biometric characteristics in terms of Relative Entropy (RE) calculated on genuine and impostor comparison scores using a Nearest Neighbour (NN) estimator. Our findings indicate that the RE is system-specific, meaning that it would be misleading to claim a universal finger vein RE estimate. We show, however, that the RE can be used to rank finger vein recognition systems (tested on the same database using the same experimental protocol) in terms of their expected recognition accuracy, and that this ranking is equivalent to that achieved using the EER. This implies that the RE estimator is a reliable indicator of the amount of discriminatory information in a finger vein recognition system. We also propose a Normalised Relative Entropy (NRE) metric to help us better understand the significance of the RE values, as well as to enable a fair benchmark of different biometric systems (tested on different databases and potentially using different experimental protocols) in terms of their RE. We discuss how the proposed NRE metric can be used as a complement to the EER in benchmarking the discriminative capabilities of different biometric systems, and we consider two potential issues that must be taken into account when calculating the RE and NRE in practice.