Since symplectic toric manifolds are well-understood, it's important to decide which Hamiltonian torus actions on symplectic manifolds can be extended to toric actions, that is, which can be obtained from a symplectic toric manifold by restricting to a subtorus. In this talk, we give necessary and sufficient conditions for a tall complexity one Hamiltonian torus action to extend to a toric action. Based in part on joint work with Karshon, and with Liu and Palmer.