Understanding the complex phenomena in the BF hearth is essential to increasing furnace productivity and to extending furnace campaign. Numerical modeling provides a cost-effective tool to obtain such knowledge. We have developed several continuum-based mathematical/numerical models to simulate the flow, heat transfer and mass transfer in the lower part of BF and in the hearth. These models have generated an improved insight into the mechanisms for liquid drainage efficiency, lining erosion and wall protection in BF hearth under operational conditions. The current paper provides an overview of these studies, as well as dealing with three specific aspects: (a) Gas flow and pressure on the liquid surface, and its effect on the drainage characteristics; (b) Flow and temperature distributions of liquid iron in the hearth, and the temperature distribution in the refractories; and (c), Titania injection to form Ti(C,N)-rich scaffolds on the hearth refractory surface, to protect the hearth from erosion.