Unlike the widely used Eulenan gas-Lagrangian particle models (particle trajectory models), two versions of two-fluid models—a pure two-fluid (FTF) model and a two-fluid-trajectory (continuum-trajectory, CT) model are proposed for simulating turbulent reacting gas-particle flows and coal combustion. Both of diem are based on Eulerian gas-phase equations, Eulenan particle-phase continuity and momentum equations, κ-ϵ-κ two-phase turbulence model, EBU-Arrhenius turbulent combustion model, six-flux radiation model, coal moisture evaporation, devolatilization and char combustion models with simultaneous three reactions. To account for the particle history effect, including the mass change due to moisture evaporation, devolatilization and char combustion and the particle temperature change due to the heat transfer between two phases, the FTF model uses Eulerian or partial differential conservation equations of particle mass, particle daf-coal mass, particle moisture and energy, while the CT model uses Lagrangian or ordinary differential equations and algebraic expressions to predict the particle mass and temperature change. Thermal NO and fuel NO formation models with a second-order moment closure to treat the turbulence-chemistry interaction are incorporated into the FTF model. Simulation of 3-D turbulent reacting gas-particle with coal combustion in sudden-expansion combustors with high-velocity jets shows that the predictions using both these two models give reasonable and qualitatively similar results. The results reveal the mechanism of fast ignition and good flame stabilization in the combustor. However, the PTF model can give more detailed information of particle flow field, for example, particle temperature and daf-coal mass field in 3-D space, than that given by the CT model. The FTF model has no difficulty in dealing with particles entering or leaving the recirculation zones, sometimes encountered in the CT model and pure particle trajectory model. The developed computer codes PERT-3 and LEAGAP-3 based on these models have already been applied in optimization design of coal burners for boiler furnaces and cement kilns