In this present paper we study geometry of compact complex man-ifolds equipped with a maximal torus T = (S 1) k action. We give two equivalent constructions providing examples of such manifolds given a simplicial fan Σ and a compelx subgroup H ⊂ T C = (C *) k. On every manifold M we define the canonical holomorphic foliation F and under additional restrictions construct transverse-Kähler form ω F. As an application of these constructions, we prove some results on geometry of manifolds M regarding its analytic subsets.