This article provides an overview of the studies on computational modeling of the vacuum arc remelting (VAR) and electroslag remelting (ESR) processes. These models involve the axisymmetric analysis of the electromagnetic, flow, heat-transfer, and phase-change phenomena to predict the pool shape and thermal history of an ingot using two-dimensional axisymmetric models for VAR and ESR. Analysis of segregation of alloying elements during solidification that gives rise to macrolevel compositional nonuniformity in titanium alloy ingots is also described. The article discusses the important features of the control-volume-based computational method to review the unique aspects of the processes. Measurement of the properties of alloys and slags is explained and an analysis of the process variants for improving the predictive accuracy of the models is presented.