The action of ArcelorMittal Maizières in the domain of physical chemistry of metallurgical slags and liquid steel has always been sustained. In particular, this activity gave birth to several models among which the cell model that describes the properties of metallurgical slags (and of liquid oxide inclusions) has a special place. This model, along with other specific models describing the metallic phases, has been included in a home-built equilibrium calculation code CEQCSI (Chemical EQuilibrium Calculations for the Steel Industry) to allow easy calculations by non specialist users. Several applications to steel elaboration will be presented. An insight into the development of new models such as the Generalized Central Atom model is also given. The application domain of this latter model is high alloyed and segregated steel grades and the same formalism is also used to improve the performance of the cell model for slags.