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Processing of metal alloys in their mushy state represents a new trend in metal processing. The process produces components with low porosity, high crack resistance along with fine microstructure and mechanical properties that are better than those produced by liquid casting, and comparable to those of forged alloys. In the present work, a summary of the current understanding on the rheology of semisolid slurries is presented. This is followed by an overview of the different mathematical models proposed by the authors to describe the experimentally observed behavior of the material, and salient numerical results including die filling.