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.