This thesis studies this existence of filling links 3-manifolds. A link L in a 3-manifold M is filling in M if, for any spine G of M disjoint from L, π_1(G) injects into π_1(M-L). Conceptually, a filling link cuts through all of the topology 3-manifold. These links were first studied by Freedman-Krushkal in the concrete case of the 3-torus M = T^3, but they leave open the question of whether a filling link actually exists in T^3. We answer this question affirmatively by proving in fact that every closed, orientable 3-manifold M with fundamental group of rank 3 contains a filling link.