Graph searching involves a team of mobile agents (called searchers or pursuers or cops) that aims at capturing a set of escaping agents (called evaders or fugitives or robbers) that hide in a network modeled by a graph. There are many variants of graph searching studied in the literature, often referred to as a pursuit-evasion game or cops and robbers game. These variants are either application driven, i.e. motivated by problems in practice, or are inspired by foundational issues at the intersection of Computer Science, Discrete Mathematics, and Artificial Inteligence. As a result, many researchers from different areas of Mathematics, Computer Science and Operations Research are interested in problems related to graph searching. GRASTA 2017 is the main forum on graph searching and was held at the Anogia Academic Village, Anogia, Crete, Greece. It gathered 39 researchers from diverse areas of Theoretical Computer Science and Discrete Mathematics related to Graph Searching Games and their Applications both from the applied and the theoretical point of view. The scientific program of the workshop consisted of 18 regular talks, and an open problem session.