Quantum computers will reshape the landscape of cryptography. On the one hand, they threaten the security of most modern cryptosystems. On the other, they offer fundamentally new ways to realize tasks that were never before thought to be possible. In this talk, I will explore the interplay between quantum computation and cryptography, and the many exciting questions at this intersection. I will describe examples that leverage quantum computers to protect against coercion in online elections, and to prevent piracy of software.