Let T be a torus, and let X be a T-space. In this talk I will relate algebraic properties of the equivariant (co)homology of X to the structure of the T-orbits in X. This generalizes a result of Atiyah and Bredon. As applications, I will characterize those compact T-manifolds which admit a Chang-Skjelbred (or GKM) description of their equivariant cohomology, and also those for which the equivariant Poincaré pairing is perfect. This is joint work with Chris Allday and Volker Puppe.