The competition and cooperation between the itinerancy behavior and localization behavior of electrons in correlated quantum materials, known as Mott physics, is the physical mechanism behind the diverse states of many quantum materials. This article reviews the manifestation of Mott physics in various quantum materials and establishes it as one of the main themes of quantum materials. Finding and understanding its ever-changing ways of manifestation is one of the central tasks of experimental research on condensed matter physics.

Specifically, the filling-control route of Mott transition is illustrated by exampling the surface K-dosed Sr₂IrO₄, which exhibits d-wave gap, pseudogap behavior in underdoped regime, and phase separation with inhomogeneous electronic state distribution. All of these show strong resemblances to the doped cuprate superconductors, another prototypical filling-control type of Mott transition case. On the other hand, the bandwidth-control route of Mott transition could be found in NiS_2–xSe_x, where its bandwidth continuously decreases with decreasing Se concentration, until it becomes an insulator. In addition, the essence of various ways of doping in iron-based superconductors is to change their bandwidths. The superconductivity shows up at intermediate bandwidth with moderate correlations, and it diminishes when the bandwidth is large and the electron correlations are weak. For heavily electron-doped iron-selenides, there is even a Mott insulator phase with strong correlations.

For carbon based materials, the phase transition between the antiferromagnetic insulator and superconducting state of A15 Cs₃C₆₀ as the volume of fullerene anions decreases could be understood in terms of a bandwidth-control Mott transition; the insulator-superconductor transition discovered in electrically gated “magic angle” twisted-angle bilayer graphene could be understood as a filling-control Mott transition.

For f electron systems, the interplay between itinerancy and localization dominates the heavy fermion behavior and their ground states. The behaviors of the f electrons are demonstrated by using the angle-resolved photoemission data of CeCoIn₅, whose f electron band becomes more coherent with decreasing temperature, and the c-f hybridization is thus enhanced and the band mass of conduction band continuously increases. The c-f hybridization behaviors of CeCoIn_5, CeIrIn₅, and CeRhIn₅ are compared with each other, and the differences in hybridization strength put their ground states into different regimes of the Doniach phase diagram. Similarly, the Skutterudites 4f² Kondo lattice system PrOs₄Sb₁₂ and its sibling 4f¹ system CeOs₄Sb₁₂ also have different ground states due to a slight difference in their c-f hybridization strengths.