In this chapter we investigate biometric key-binding systems for i.i.d. Gaussian biometric sources. In these systems two terminals observe two correlated biometric sequences. Moreover, a secret key, which is independent of the biometric sequences, is selected at the first terminal. The first terminal binds this secret key to the observed biometric sequence and communicates it to the second terminal by sending a public message. This message should only contain a negligible amount of information about the secret key. Here, in addition, we require it to leak as little as possible about the biometric data. For this setting the fundamental trade-off between secret-key rate and privacy-leakage rate is determined. Moreover, we investigate the effect of binary quantization on the system performance. We further discuss the popular fuzzy commitment scheme. It is shown that from the perspective of privacy leakage, there are better options for fuzzy commitment than its typical implementation based on BCH codes.