The ironmaking blast furnace (BF) remains the most significant and important process for the production of liquid iron. For the achievement of stable furnace operation and good performance, mathematical modellings at different levels increasingly become a powerful tool in developing better understanding of this multiphase flow system, in particular the gas-solid flow. This thesis represents an effort in this area. A simplified and continuum-based mathematical model is proposed and tested to predict the BF gas-solid flow at a macroscopic level. The results show that the simple model is able to predict the general features of the solid flow, including the effects of gas and solid flowrates, and materials properties. The simplified model can be readily implemented in a full process model that needs to have a quick response to change for the purpose of control and optimization. To overcome the difficulties encountered in continuum modelling, i.e. determination of constitutive correlations, and particularly the description of the stagnant zone when related to BF, a discrete model based on the coupling approach of discrete element method (DEM) and computational fluid dynamics (CFD) is then employed to investigate the gas-solid flow in a model BF at a microscopic level. The results confirm the effects of variables such as gas flow rate, solid flow rate, particle properties, and model types. More importantly, such an approach can generate abundant microscopic information such as flow structure (particle velocity, porosity, coordination number) and force structure, which are of paramount importance to elucidate the gas-solid flow mechanisms, and develop a more comprehensive understanding of BF gas-solid flow, such as the formation mechanism of the stagnant zone. Further, the transient gas-solid flow phenomena, together with the considerations of cohesive zones and hearth liquid, can be predicted. Further, in order to develop understanding of thermal behaviour and elucidate the heat transfer mechanisms occurring in particle-fluid flow system, a new model is proposed by extending the DEM-CFD, and then tested in gas fluidization. The model considers the three heat transfer modes, and demonstrates its ability in investigating the heat transfer mechanisms, and offers an effective method to elucidate the mechanisms governing the heat transfer in particle-fluid systems at a particle scale. It is recommended to apply to the study of BF thermal behaviour.