Recent progress in confined atoms and molecules: Superintegrability and symmetry breakings

This review article has the antecedents of Jaskolski's 1996 Physics Report on Confined Many-electron Systems, the fifteen chapters on the Theory of Confined Quantum Systems in Vols. 57 and 58 of 2009 Advances in Quantum Chemistry, and the nine chapters of the 2014 Monograph Electronic Structure of Confined Quantum Atoms and Molecules. In this contribution, the last two sets of reviews are taken as points of reference to illustrate some advances in several lines of research in the elapsed periods. The recent progress is illustrated on the basis of a selection of references from the literature taking into account the confined quantum systems, the confining environments and their modelings; their properties and processes, emphasizing the changes due to the confinement; the methods of analysis and solutions, their results including confiability and accuracy; as well as applications in other areas. The updated and current works of the Reviewer are also presented. The complementary words in the title apply to the simplest atom in its free configuration and to the harmonic oscillator quantum dot, because they admit more exact solutions than the number of their degrees of freedom; and to their many-electron and confined counterparts, due to their additional interactions and changes in boundary conditions.