Twisting graphene into correlation and topology

Twisted graphene moiré superlattices have emerged as a highly tunable platform in which electronic correlation and band topology intertwine in unprecedented ways. Near the magic angle, moiré interference dramatically suppresses kinetic energy, producing flat electronic bands with nontrivial quantum geometry and multiple internal degrees of freedom. These features enable interaction-driven phases that have no direct analogue in conventional solids. In this Review, we survey recent progress on magic-angle twisted bilayer graphene and related twisted multilayer graphene systems, focusing on how many-body and topological effects reconstruct the flat-band spectrum and organize the observed phase diagram. We discuss correlated insulating states, flavor-selective cascades, intervalley coherent orders, and the coexistence of localized moments with itinerant carriers. We further examine the emergence of topological phases-including orbital Chern insulators, fractional Chern insulators, and topological electronic crystals-that arise from the interplay between interactions and band topology. Superconductivity in twisted graphene is reviewed as a strongly coupled, unconventional phenomenon, shaped by both electronic correlation and quantum geometry. The discussion is then extended to twisted multilayer graphene architectures, highlighting the intertwined electronic correlation and band topology, and their influence on superconductivity. We conclude by outlining key open problems in superconductivity and opportunities for engineering novel correlated and topological states in twisted graphene moiré systems.