Irreversibility refers to the degree of difficulty faced by an adversary in recovering the unprotected biometric features from the protected templates stored in a Biometric Template Protection (BTP) system. Irreversibility is a vital privacy consideration in the design of BTP systems. In this chapter, we attempt to characterize irreversibility in a systematic way. We explain the concept of irreversibility, justify its importance, and describe approaches to measure it. We begin with theoretical measures of irreversibility derived from information theory. We argue that a suitable information-theoretic irreversibility metric is the number of bits of information about the unprotected template revealed by the protected template. Next, we consider measures of irreversibility based on cryptography, particularly for BTP systems enabled by homomorphic cryptosystems. We then discuss irreversibility of BTP systems based on feature transformations applied to the unprotected template. These transformations include salting-based transformations, non-invertible transformations, and neural network-based mappings. In practice, few BTP implementations lend themselves to a clean, theoretical characterization of irreversibility, and the property has to be measured empirically. We review challenges associated with empirical measurements of irreversibility, and we also describe some best practices to ensure that the empirical irreversibility metrics are meaningful and applicable. Finally, we consider irreversibility in cases where a given user has protected templates stored on several BTP systems.