I will give a light introduction to the theory of quantum graphs. Quantum graphs are non-commutative generalizations of finite graphs that arise naturally in many areas, including the study of zero-error capacities of quantum channels, quantum symmetry groups of graphs, and in the theory of non-local games. I will give an overview of some of these connections and explain some ongoing joint work with Kari Eifler, Christian Voigt and Moritz Weber, where we generalize the well-known graph $C^\ast$-algebra construction to the setting of quantum graphs.