2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227991I survey theoretical advances in our understanding of the quantum phases and phase transitions of Mott insulators, and of allied conducting systems obtained by doping charge carriers. A number of new experimental examples of Mott insulators have appeared in recent years, and I critically compare their observed properties with the theoretical expectations.29 pages, 13 figures; Rapporteur talk at the 24th Solvay Conference on Physics, "Quantum Theory of Condensed Matter", Brussels, Oct 2008; (v2+v3+v4) added refs and clarifications; v5: added figure testing theory of pressure-tuned QPT in a dimerized antiferromagnet; v6: added refsStrongly Correlated ElectronsHigh Energy Physics - Theorytext