When we encode information into physical systems that are small enough to be governed by the laws of quantum mechanics, a large part of our intuition about how information behaves goes out the window-- for example, information can no longer be copied perfectly. This has far-reaching implications in several areas of computer science, including cryptography, where it changes the rules of the game for both honest participants and potential attackers. In this talk, I will present an overview of quantum cryptography and how my own work fits in the picture. I will also give a glimpse of some of the mathematical techniques that recur frequently in my work, namely methods from "one-shot" information theory, and methods for computing on encrypted quantum data