  We introduce and study a special class of Kato manifolds, which we call toric
Kato manifolds. Their construction stems from toric geometry, as their
universal covers are open subsets of toric algebraic varieties of non-finite
type. This generalizes previous constructions of Tsuchihashi and Oda, and in
complex dimension 2, retrieves the properly blown-up Inoue surfaces. We study
the topological and analytical properties of toric Kato manifolds and link
certain invariants to natural combinatorial data coming from the toric
construction. Moreover, we produce families of flat degenerations of any toric
Kato manifold, which serve as an essential tool in computing their Hodge
numbers. In the last part, we study the Hermitian geometry of Kato manifolds.
We give a characterization result for the existence of locally conformally
K\"ahler metrics on any Kato manifold. Finally, we prove that no Kato manifold
carries balanced metrics and that a large class of toric Kato manifolds of
complex dimension $\geq 3$ do not support pluriclosed metrics.
