We discuss the main features of a phase space noncommutative model of quantum mechanics and its application for quantum cosmology and black holes in the context of the Kantowski-Sachs minisuperspace geometry. References: hep-th/0505064; hep-th/0509207; gr-qc/0606131; hep-th/0611257; arXiv:0712.4122; arXiv:0907.1818; arXiv:0912.4027