I will discuss a collection of recent results on both linear and nonlinear results on discrete and quantum graphs. First I will discuss results related to spectral theory for the (possibly magnetic) Laplacian on a variety of graphs that relates to work with Berkolaiko, Canzani, Cox, Weinstein and others. I will also discuss nonlinear equations on graphs that comprises work with Bandres, Berkolaiko, Osting, Pelinovsky, Rechtsman,  and others.