Biometric recognition as an efficient and hard-to-forge way of identification and verification has become an indispensable part of the current digital world. The fast evolution of this technology has been a strong incentive for integration into many applications. Meanwhile, blockchain, the decentralized ledger technology, has been widely received by both research and industry in the past few years, and it is being increasingly deployed today in many different applications, such as money transfer, IoT, healthcare, or logistics. Recently, researchers have started to speculate on the pros and cons and what the best applications would be when these two technologies cross paths. This paper provides a survey of the research literature on the combination of blockchain and biometrics and includes a first legal analysis of this integration based on GDPR to shed light on challenges and potentials. Although the integration of blockchain technology into the biometric sector is still in its infancy, with a growing body of literature discussing specific applications and advanced technological setups, this paper aims to provide a holistic understanding of blockchain applicability in biometrics. Based on published studies, this article discusses, among others, practical examples combining blockchain and biometrics for novel applications in PKI systems, distributed trusted services, and identity management. Challenges and limitations when combining blockchain and biometrics that motivate future work will also be discussed; e.g., blockchain networks at their current stage may not be efficient or economical for some real-time biometric applications. Finally, we also discuss key legal aspects of the EU General Data Protection Regulation (GDPR) related to this combination of technologies (blockchain and biometrics); for example, accountability, immutability, anonymity, and data protection elements.