I will go over recent advances in two-party secure computation involving branching programs: where one party holds a branching program P and the other party holds an input x, and the goal is for the two parties to jointly compute P(x) without revealing any other information. I will mention applications of these results to such areas as Private Set Intersection (PSI) and Private-Information Retrieval (PIR). Such PSI and PIR protocols are used as critical components of various privacy-preserving technologies, such as those for contact tracing, password breaching, etc.