This article provides an overview of the models of two induction heating devices, namely, induction crucible furnace (ICF) and induction furnace with slits, or segmented and water-cooled induction furnace with cold crucible (IFCC). These devices are used for melting with skull formation of low-conductivity materials such as glasses and oxides. The article presents the governing equations and boundary conditions for ICF and IFCC modeling. It includes a discussion on three electromagnetic field models in IFCC, namely, two-dimensional (2-D), quasi-three-dimensional, and three-dimensional (3-D) models. The article provides information on the simulation of skull formation in IFCC, and elucidates the transient axisymmetrical 2-D model and the transient 3-D model, including the primary results achieved for both glasses and skull formation.