The ZX calculus is a graph-based semantics for quantum circuits that supports equivalence reasoning based on a small set of local equations. Compared to traditional semantics for quantum circuits, the ZX calculus is better suited to a number of automated analyses. And the equational theory is simple enough to illustrate properties of key quantum circuits like quantum teleportation and magic state injection circuits by hand. This talk introduces the ZX calculus and shows how it can aid in understanding quantum computing.