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A review of black-box models for short-term time-discrete prediction of the silicon content of hot metal produced in blast furnaces is presented. The review is primarily focused on work presented in journal papers, but still includes some early conference papers (published before 1990) which have a clear contribution to the field. Linear and nonlinear models are treated separately, and within each group a rough subdivision according to the model type is made. Within each subsection the models are treated (almost) chronologically, presenting the principle behind the modeling approach, the signals used and the main findings in terms of accuracy and usefulness. Finally, in the final section the approaches are discussed and some potential lines of future research are proposed. In an Appendix , a list of commonly used input and output variables in the models is presented.