The concept of homomorphic encryption was introduced almost exactly same time as the first public-key cryptographic algorithm RSA, which was multiplicatively homomorphic. Encryption functions with additive and multiplicative homomorphisms allow us (at least in principle) to securely compute any function, and thus are highly desired. Homomorphic encryption functions applied to machine learning scenarios have applications in healthcare, finance, and national security. Since the work of Craig Gentry, there have been several homomorphic encryption proposals, however, their time and space requirements do not give way to acceptably efficient implementations in real-world scenarios. In this talk, I will explain the use of homomorphic encryption in machine learning, and describe some of algorithmic and architectural challenges facing the implementors.