Computational studies of steelmaking tundish systems date back to early eighties. Two independent overviews, published, respectively, in 1999 and 2010, summarize a large number of research work reported by various groups of investigators. These indicate that modeling of tundish metallurgy is primarily restricted to the steady operating period, and phenomena such as, fluid flow, turbulence, thermal and material mixing, inclusion floatation, and removal etc. are given wide attention. Toward this, homogeneous, turbulent flow modeling is relatively more frequent. Since 2008 or so, transient and multi‐phase modeling of tundish metallurgy are popular and reported by some groups of investigators. This paper presents a brief summary and a critical assessment of such efforts vis a vis industrial tundish metallurgy practices. Despite advancements in theory and powerful computational procedures, it is brought out that progress in mathematical modeling of tundish metallurgy, particularly during the last decade, is somewhat sluggish. In the final section of the manuscript, an account of continuing efforts of the author and his associates are presented, wherein, modeling of two phase flows in ladle shroud and latter's attendant influences on the metallurgical performance of steelmaking tundish is discussed.