The directed landscape is a random directed metric on the plane that is the scaling limit for models in the KPZ universality class (i.e. last passage percolation on $\mathbb{Z}^2$, TASEP). In this metric, typical pairs of points are connected by a unique geodesic.  However, certain exceptional pairs are connected by more exotic geodesic networks. The goal of this talk is to describe a full classification for these exceptional pairs.