In the early 70’s, the concept of “expander graphs” was introduced as an optimal model for networks of arbitrary size. Back then, it was not even known whether such graphs exist or not. Today, we not only know that they exist, but have seen their importance come up in a great spectrum of fields in mathematics and computer science. In this talk, we will explore what these graphs are and give an idea about how they have recently made a splash on the number theory scene.