Rapid development of the copper-catalyzed amination of aryl halides in the beginning of the 21st century, known as the Renaissance of the Ullmann chemistry, laid foundations for the use of this method as a powerful tool for the construction of the C(sp2)-N bond and became a rival of the Buchwald–Hartwig amination reaction. Various applications of this approach are well-documented in a number of comprehensive and more specialized reviews, and this overview in the form of a personal account of the Cu-catalyzed arylation and heteroarylation of the adamantane-containing amines, and di- and polyamines, covers a more specific area, showing the possibilities of the method and outlining general regularities, considering reagents structure, copper source and ligands, scope, and limitations. The material of the last decade is mainly considered, and recent data on the application of the unsupported copper nanoparticles and possibilities of the Chan-Lam reaction as an alternative to the use of aryl halides are also discussed.