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The available studies in the literature on mathematical modeling of the vacuum circulation (RH) refining process of moltensteel have briefly been reviewed. The latest advances obtained by the author with his research group have been summarized. On thebasis of the mass and momentum balances in the system, a new mathematical model for decarburization and degassing during the RHand RH-KTB refining processes of molten steel was proposed and developed. The refining roles of the three reaction sites, i.e. theup-snorkel zone, the droplet group and steel bath in the vacuum vessel, were considered in the model. It was assumed that the masstransfer of reactive components in the molten steel is the rate control step of the refining reactions. And the friction losses and dragsof flows in the snorkels and vacuum vessel were all counted. The model was applied to the refining of molten steel in a multifunctionRH degasser of 90 t capacity. The decarburization and degassing processes in the degasser under the RH and RH-KTB operating condi-tions were modeled and analyzed using this model. Besides, proceeded from the two-resistance mass transfer theory and the mass bal-ance of sulphur in the system, a kinetic model for the desulphurization by powder injection and blowing in the RH refining of moltensteel was developed. Modeling and predictions of the process of injecting and blowing the lime based powder flux under assumed oper-ating modes with the different initial contents of sulphur and amounts of powder injected and blown in a RH degasser of 300 t capacitywere carried out using the model. It was demonstrated that for the RH and RH-KTB refining processes, and the desulphurization bypowder injection and blowing in the RH refining, the results predicted by the models were all in good agreement respectively with datafrom industrial experiments and practice. These models may be expected to offer some useful information and a reliable basis for de-termining and optimizing the technologies of the RH and RH-KTB refining and desulphurization by powder injection and blowing in theRH refining and for controlling the processes.