Abstract: We are going to outline the structure of the category of the Gorenstein projective modules for a Nakayama algebra A. As a main tool we introduce the resolution quiver of A, it provides a fast algorithm in order to obtain the Gorenstein projective modules and to decide whether A is a Gorenstein algebra or not, and whether it is CM-free or not. It seems to be of interest that the resolution quiver of a connected Nakayama algebra either has no loops or else all cycles are loops.