With the advent of modern technology, the use of biometric authentication systems has been on the rise. The core of any biometric system consists of a database which contains the biometric traits of the successfully enrolled users. As such, maintenance of the security of the database is paramount, i.e. it must be made sure that the contents of the database should not be compromised to foreign threats or adversaries. Biometric encryption (BE) is by far the most successfully studied and analysed technique used for providing this required level of security in biometric systems. In this survey, we discuss the intuition behind this idea and study in deep the key-binding-based mechanisms of BE which will provide a basic foundation for future novel researches in this area. In addition to the latest available survey, our paper investigates in details the core ideas behind the development of the fuzzy frameworks and includes the most recent works in the available literature. This study is concluded by inspecting the merging of multimodal biometrics with the fuzzy systems and discussing some open challenges in this domain.