This is a follow-up on Jayden's talk. Tropical Grassmannians are polyhedral fans and we introduce how to construct a polyhedral complex that captures their combinatorics. In the case k=2 (Grassmannian of lines), we establish an isomorphism between this polyhedral complex and the simplicial complex of phylogenetic trees. We also establish a one-to-one correspondence between the tropical Grassmannian and a subset of the Dressian given by tropical linear spaces of "realizable" valuated matroids.