Expander graphs in general, and Ramanujan graphs in particular, have been a focused of a lot of research in the last five decades. It has been probably the area with the most fruitful interaction between mathematics and computer science, where applications  went both ways. In recent years a high dimensional theory of expanders have started to emerge.

We will survey some its its challenges and achievements and try to explain why this is not just a generalization but also an area which lead to new horizons in pure math ( e.g. topological overlapping) and in CS ( “property testing”).