Considerable efforts have been made in academia and industry over the last two decades to fully exploit and enhance the metallurgical performance of continuous casting tundish systems. Towards these goals, numerous physical and mathematical modelling studies embodying both industrial and water model tundishes have been carried out and reported in the literature. Based on an extensive literature search, we now present a summary, discussion and analysis of these. For the sake of convenience and clarity of presentation, the studies have been categorised into three major groups: (1) physical modelling (2) mathematical modelling and (3) combined physical and mathematical modelling. In each of these categories, a great number of publications on various aspects of tundish metallurgy, such as, modelling criteria, turbulent fluid flow, residence time distributions (RTD), inclusion transport and separation, heat loss and temperature drop, grade transition and intermixing, etc. have been reported. These works have lead to considerable improvements in our understanding of the various transport processes (viz, RTD, inclusion float out, thermal energy transport, etc.) associated with tundish operations. Comprehensive and sufficiently reliable mathematical models are also currently available and these also allow one to carry out full scale predictions and useful engineering design and process calculations. None the less, certain obscurities and uncertainties remain. These are reviewed together with suggestions of areas where further research is needed.