While the laws of quantum mechanics have been known for almost ninety years, we are still learning what they allow. One surprise in recent years has been the discovery of “topologically-protected” quantum states of matter, in which “entanglement” plays a key role, and ensures that unexpectedly-robust surface states occur at the boundary between “topological” and “ordinary” regions (the so-called “bulk-boundary correspondence”). Information hidden non-locally in the entanglement may provide a route to “topologically-protected” quantum information processing. A recent surprise has been that some non-quantum aspects of these properties can also survive in classical systems involving waves and oscillations (photonics and mechanical systems).