Contact toric manifolds

We provide a complete and self-contained classification of (compact connected) contact toric manifolds thereby finishing the work initiated by Banyaga and Molino and by Galicki and Boyer. Our motivation comes from the conjectures of Toth and Zelditch on the uniqueness of toric integrable actions on the punctured cotangent bundles on n-toru 𝕋n and of the two-sphere S2. The conjectures are equivalent to the uniqueness, up to conjugation, of maximal tori in the contactomorphism groups of the cosphere bundles of 𝕋n and S2 respectively.