In cryptography, performing computations on encrypted material without first decrypting it has long been an aspiration. This is exactly what homomorphic encryption (HE) accomplishes. By allowing computation on encrypted data, the associated privacy and security of sensitive information are beyond imagination to date. This chapter delves into the vast and intricate realm of HE, its fundamental theories, and far-reaching implications for machine learning. As a result of the sensitive nature of the data on which machine learning is based, privacy and security issues often arise. In this vein, homomorphic encryption, which allows algorithms to learn from and predict encrypted data, emerges as a possible panacea. The authors thus set out in this chapter to prepare the ground for a deeper understanding of that synergy, showing how it is there but also what lies ahead.