Biometric systems are witnessing widespread adoption driven by (1) significant advances made in AI and, more specifically, deep learning, (2) growth in application scenarios that adopt biometrics technology, and (3) growth in cloud services that host biometric applications. This trifecta of changes calls for re-evaluating the threat model related to biometrics system operation—for example, the threats and risks when a biometrics system is hosted on a cloud increase significantly. Similarly, the underlying deep model training and deployment introduces new types of attacks. Therefore, it is imperative to consider the challenges that now come to the fore, including privacy and security. In this chapter, we extend well-known past biometrics threat models to include attacks that may be attributed to deep machine learning models and the associated cloud services. The chapter outlines the critical security and privacy vulnerabilities of modern biometric systems and the role of homomorphic encryption in mitigating these vulnerabilities. Specifically, we elucidate the opportunities and challenges of employing homomorphic encryption to secure biometric templates.