The commercial incentives to obtain improved control of the steelmaking process in the electric-arc furnace are presented, and the progress made in applying computer control is reviewed. The development of a mathematical model of the refining process is shown to be restricted by the complex metallurgical nature of the process and the deficiency of existing plant instrumentation. The ability of a mathematical model, evolved from theoretical considerations, to simulate, accurately, a limited class of operating practice is demonstrated. A compromise between complexity and implied certainty of the model is obtained by a reduction in the dimension of the model state vector, and by the introduction of a white-Gaussian-noise process to account for the effect of the ignored states and the hypotheses on which the model is developed. Techniques developed recently for obtaining noisecorrupted measurements of the carbon content and temperature of the process are investigated, and the statistics of the uncertainty of these measurements is determined. The implementation of the extended Kalman filter for online state estimation is considered, and the operation of the filter under varied conditions of uncertainty is discussed. A technique for controlling divergence of the filter algorithm is presented, and the results of simulations indicate that estimates of the states can be obtained to the accuracy required for the design of a refining control strategy.