A lecture given by Tarashankar DebRoy, at the Adventures in the Physical Metallurgy of Steels (APMS) conference held in Cambridge University. Mathematical modelling of the friction stir welding of steels. In previous work, we have established a scheme that exploits a combination of three-dimensional heat and mass flow models, together with fast calculation algorithms and damage accumulation models, to assess tool durability and define the domains of satisfactory tool life in the context of welding difficult aluminium alloys. We now apply this scheme to the friction stir welding of steel, and extend the calculations to cover consequences on the microstructure of the steel while optimizing tool life. This is the first model which covers both the processing parameters and the consequences on the physical metallurgy of the steel.