Abstract: Under the "dual-carbon" target framework, coal-fired boilers are confronted with the twin imperatives of deep energy conservation and emissions reduction alongside flexible operational capability. Combustion numeri-cal simulation based on computational fluid dynamics (CFD), by virtue of its capacity to resolve complex physicochemical processes within the furnace, has emerged as a critical technical methodology underpinning boiler design and operational optimization. This paper presents a systematic review of research advances in the field of pulverized coal boiler combustion numerical simulation, encompassing the following principal aspects: (1) sub-models and their applicable ranges, including models for particle transport and turbulent flow, gas-phase combustion, volatile release, char combustion, radiative heat transfer, and NOx formation; (2) advances in CFD applications for flexible load-following and combustion optimization, with emphasis on combustion efficiency enhancement, thermal deviation suppression, and flue gas recirculation control; (3) modeling frameworks for ash and slag deposition simulation that integrate particle transport, adhesion criteria, deposit growth, and heat transfer feedback; (4) quantitative evaluation indices for low-load flame stabiliza-tion and optimization strategies encompassing burner configuration, air distribution, and operational parame-ter adjustment; (5) three coupling paradigms for furnace combustion and hydrodynamic interaction modeling, namely independent simulation, one-way coupling, and two-way coupling, along with their respective appli-cable scenarios; (6) novel modeling requirements introduced by biomass co-firing in coal-fired boilers, in-cluding non-spherical particle dynamics, thermochemical conversion kinetics, NOx reburning reduction, and ash deposition behavior; and (7) detailed chemical reaction kinetics, NOx formation mechanisms, and com-bustion characteristics under hydrogen and ammonia co-firing conditions. In the ongoing transition toward flexible and low-carbon operation, the existing numerical modeling framework has progressively matured, yet a fundamental trade-off between predictive accuracy and computational cost remains to be resolved. Re-fined characterization of boundary conditions represents a critical direction, particularly with respect to ash and slag deposition as well as combustion and hydrodynamic coupling simulations. Furthermore, the non-spherical particle dynamics, thermochemical conversion kinetics, and ash deposition phenomena associated with biomass co-firing, together with the demands imposed by hydrogen and ammonia co-firing on detailed chemical kinetics and NOx prediction capability, collectively present substantial challenges to existing mod-eling approaches. Finally, prospective research directions are identified in three areas: multi-fuel co-combustion modeling, multi-process coupling and process-evolution prediction, and the integration of CFD with artificial intelligence techniques.