This paper aims to present a review of numerical models for the gas-steel-slag three-phase flow in gas-stirred ladles. The modeling frameworks is classified as: mixture model, interfacial model, multi-fluid model and Eulerian-Lagrangian (EL) model. The interfacial model is good at simulating the interfacial structure among phases, while the multi-fluid model is suited for systems consist of different kinds of phases as it separately solves the constitutive equations of each phase with modeling their interactions. Recently, the Eulerian-Lagrangian model is frequently adopted to make the discrete phase more comprehensively resolved. With coupling the interfacial model, the interfacial-Eulerian-Lagrangian (IEL) model shows a good suitability to simulate the gas-steel-slag three-phase flow, and the discrete-continuum transition, regarded as a multiscale approach, is very helpful for revealing the bubble behavior. Moreover, other phenomena including the heat and mass transfer, the erosion at the liquid-solid interface, etc. are still lack of investigation by comprehensive models. (c) 2020 Elsevier B.V. All rights reserved.