Random graphs and hypergraphs have long been employed as network models for a bevy of machine learning problems, from clustering and community detection to coding theory, signal processing, and so on. The spectral properties of regular models, in particular things like the spectral gap, have often played an important role in such applications. In this wide-audience talk, I will mention some of the random matrix techniques used in the analysis of spectral gap in such regular structures, as well as some of the challenges and open problems.