In order to guarantee better user-friendliness and higher accuracy, beyond the existing traditional single-factor biometric systems, the multimodal ones appear to be more promising. Two or more biometric measurements for the same identity are extracted, stored and compared during the enrollment, authentication and identification processes. Deployed multimodal biometric systems also referred to as multibiometrics or even as multimodalities are commonly found and used in electronic chips, embedded in travel documents. The widespread use of such systems, the nature of the shared data and the importance of applications introduce privacy risks. A significant number of approaches and very recent advances to the relevant protection technologies have been published. This paper illustrates a comprehensive overview of research in multibiometrics, the protection of their templates and the privacy issues that arise. Up-to-date review of the existing literature revealing the current state-of-art suggestions is provided, based on the different levels of fusion and the employed protection algorithms, while an outlook to future prospects is also discussed.