The topic of this special issue deals with a subject matter that has been receiving immense attention from various research communities, and not only within the signal processing community. Discusses research and development in the area of the adaption and learning over complex network systems. Extensive research efforts on information processing over graphs exist within other fields such as statistics, computer science, optimization, control, economics, machine learning, biological sciences, and social sciences. Different fields tend to emphasize different aspects and challenges; nevertheless, opportunities for mutual cooperation are abundantly clear, and the role that signal processing plays in this domain is of fundamental importance.