Homomorphic encryption is an encryption method to allow arbitrary computation on encrypted data without decryption. It has emerged as one of the promising solutions to address privacy issues in computation over sensitive data. In this talk, I will introduce recent development and progress on homomorphic encryption. We then proceed to review the techniques such as secure matrix computation, multi-key homomorphic encryption, and integration with secure multi-party computation. We conclude with the state-of-art benchmarks of the encryption systems in real-world applications such as machine learning and biomedical study.​