In many-electron systems, strong correlations lead to a rich variety of quantum phases and exotic phenomena. In this thesis, we investigate several such effects, including quantum criticality, unconventional superconductivity, and topology. Three general directions of investigation have been pursued. The first direction focuses on the Kondo-destruction quantum critical point of heavy-fermion metals, a prototype class of systems with strong correlations. We demonstrate non-trivial Kondo entanglement and dynamical scaling in the spin susceptibility. In addition, we show that robust superconductivity develops out of the quantum critical normal state that features a large-to-small Fermi-surface transformation. The second direction of research explores the interplay between electron correlations and topology. We find that a charge-spin intertwined phase is stabilized by the cooperation of topology and correlations. Furthermore, we analyze topological phases in the non-Fermi liquid context. Via interacting Green’s function, we determine the constraint of space-group symmetry on correlated topology and identify a gapless topological state without free-electron counterpart. Finally, we investigate the correlation effect in different multiorbital systems, including iron-based superconductors, UTe2, and moir´e graphene.