Quantum systems are notoriously unpredictable. Whether Schrödinger’s cat will end up dead or alive is as unpredictable as a coin flip. On the other hand, if you don’t go in and measure things, quantum systems evolve in an apparently very simple way, according to the Schrödinger equation. This apparent simplicity hides the potential for enormous complexity in the relationships between subsystems and how those relationships evolve in time. The complexity of a subsystem and its relation to the whole can be quantified in a variety of ways. I’ll describe some of them currently in use, including the entanglement entropy and the quantum circuit complexity. Then, I’ll present a new quantity that I’m working on, called the local quantum complexity, and how it may be applied to some example systems. I’ll also explain how this work is motivated by the strange fact that black holes are the simplest objects in nature, at large scales, while possibly also the most complex, at microscopic scales. In the last part of my talk, I’ll talk about something completely different: my work with the Physicists’ Coalition for Nuclear Threat Reduction.