Let $M$ be a connected smooth manifold equipped with an effective smooth action of a compact torus $G$. Then we can see that $\dim G_x + \dim G \leq \dim M$ for all $x \in M$, where $G_x$ denotes the isotropy subgroup of $G$ at $x$. We say that the action of $G$ on $M$ is maximal if the equality holds for some $x \in M$. In this talk I will explain that the category of compact complex manifolds with maximal torus actions (with equivariant holomorphic maps as morphisms) is equivalent to the category of certain pairs of nonsingular fans and vector spaces. If time allows, I will explain canonical foliations on compact complex manifolds with maximal torus actions.