Excitable media are characterized by the ability to propagate waves of activity in an intermittent fashion, subject to the emergence of refractory states. Several examples of biomaterials and biosystems can be modelled as excitable media, where refractory states emerge naturally as a form of chemical exhaustion. While models of excitable dynamics have been extended to heterogenous network structures, lacking the Euclidean metric of a lattice, the emergence of waves in such systems is far less understood. I will review some recent results on the study of wave patterns in highly heterogeneous network structures, relevant for instance to the problem of activity propagation in the brain, showing how techniques originally devised for materials can help understand how global activity patterns emerge from localized sources in heterogenous biosystems.