The papers in this special issue are intended to address some of the main research challenges in Graph Signal Processing by presenting a collection of the latest advances in the domain. These papers examine key representation, learning and processing aspects for signals living on graphs and networks, as well as new methods and applications in graph signal processing. Numerous applications rely on the processing of high dimensional data that reside on irregular or otherwise unordered structures that are naturally modeled as networks. The need for new tools to process such data has led to the emergence of the field of graph signal processing, which merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process signals on structures such as graphs. This important new paradigm in signal processing research, coupled with its numerous applications in very different domains, has fueled the rapid development of an inter-disciplinary research community that has been working on theoretical aspects of graph signal processing and applications to diverse problems such as big data analysis, coding and compression of 3D point clouds, biological data processing, and brain network analysis.