An overview of the (CuY)-Y-I/II material is performed on the basis of the results obtained during the last 5 years on their structure (nature of the Cu species, siting, coordination...), their use and reactivity, based on TPR, XRD and various ex situ and in situ spectroscopies such as XAS, IR and EPR. A brief summary of previous work is reported to position these recent advances in the context of three decades of studies devoted to the characterization of these materials. Quantum mechanics modeling of both the structure and reactivity of the material is also reported, providing complementary information. Insights related to the properties of the catalysts obtained recently using this molecular approach are presented to demonstrate that this material behaves as a supermolecule. In addition to its adsorption properties, the zeolite Y is one of the most popular zeolite used in catalysis. When it is exchanged with copper, in selective adsorption processes, it has been shown to be a promising adsorbent in the desulfurization of transportation fuels. In the area of environmental applications, a new catalyst based on CuY zeolite is now used for NOx removal from the tail gas of nitric acid plants. Some selected examples are given to illustrate some of the CuY zeolite properties such as adsorption, deNO(x) elimination and biomimetic behavior.