The broad research thematic of flows on networks was addressed in recent years by many researchers, in the area of applied mathematics, with new models based on partial differential equations. The latter brought a significantcant innovation in a field previously dominated by more classical techniques from discrete mathematics or methods based on ordinary differential equations. In particular, a number of results, dealing with vehicular traffic, supply chains and data networks, have been presented recently. The field seems still to flourish and a considerable number of papers devoted to the subject is published every year, also because of the wide and increasing range of applications: from blood flow to air traffic management. The aim of the present survey talk is to present a view on large number of themes, results and applications related to this broad research direction. These techniques can be applied to different fields from mathematical modeling, analysis, numerics, optimization. We will provide an overview as well as some in-depth results.