From the backgrounds of the recent trends towards low reducing agent operation of large blast furnaces and application of diversified charging modes for various burdens, an advanced mathematical model of the blast furnace is required. Although conventional models based on the continuum model have been widely used, these models are not sufficient for the recent demands. Discrete models such as discrete element model (DEM) and particle method are expected to enable precisely simulation of the discontinuous and inhomogeneous phenomena in the recent operating conditions. With discrete models, microscopic information on each particle in the packed bed can be obtained in addition to the overall phenomena in the blast furnace. Visual information for understanding in-furnace phenomena can be also obtained with high spatial resolution. Liquid dripping and the movement of fines in the lower part of the blast furnace can be simulated with high accuracy by using DEM and particle methods such as the Moving Particle Semi-implicit Method (MPS). Moreover, the optimum bed structure for low reducing agent operation is being clarified by application of the Eulerian-Lagrangian method. This review summarizes recent progress on the mathematical models based on the discrete model.