Planar Graph TSP is the problem of finding the shortest tour that visits all vertices of a planar unweighted graph at least once. The talk will present a polynomial time approximation scheme (PTAS) for this problem developed by Grigni, Koutsoupias and Papadimitriou (presented in 1995 FOCS). The approximation scheme uses a planar separator theorem to divide the graph into subproblems. We will discuss the proof of the original planar separator theorem and several modifications that allow it to be used for this problem.