Let $p$ be a prime number. In classical Iwasawa theory, we are interested in the study of arithmetic objects arising from $p$-adic Lie extensions of number fields. Recently, several concepts originating from classical Iwasawa theory have found extension to towers of graph coverings. This talk will begin with a review of these recent advances. I will explain how isogeny graphs, enhanced with level structures, provide explicit examples that fit into the framework of Iwasawa theory of graph coverings. The talk will conclude with an overview of the "volcanic" structure of these graphs. This is joint work with Katharina Mueller.