The articles in this special section focus on graph signal processing. Generically, the networks that sustain our societies can be understood as complex systems formed by multiple nodes, where global network behavior arises from local interactions between connected nodes. More succinctly, a network or a graph can be defined as a structure that encodes relationships between pairs of elements of a set. The simplicity of this definition drives the application of graphs and networks to a wide variety of disciplines, such as biology, medicine, psychology, sociology, economics, engineering, computer science, and so on.