2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158830We give an expository account of a conjecture, developed by Coates--Corti--Iritani--Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold X to the quantum cohomology of a crepant resolution Y of X. We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan--Graber. We also give a "quantized" version of the conjecture, which determines higher-genus Gromov--Witten invariants of X from those of Y.34 pages. Version 2: added a paragraph (Remark 4.2) clarifying the history and origins of the conjecture. Version 3: corrected some typos in Section 8Algebraic GeometryMathematical Physics14N35 (Primary); 14A20, 83E30 (Secondary)text