This talk concerns toric Hamiltonian actions with momentum maps taking values in regular Poisson manifolds of compact type, or more precisely: toric Hamiltonian actions of regular and proper symplectic groupoids. Examples of these include symplectic toric manifolds, proper Lagrangian fibrations and proper isotropic realizations of Poisson manifolds of compact type. The aim will be to explain the classification of such toric actions in terms of "Delzant polytopes" in the leaf space of the symplectic groupoid.
