This chapter provides a detailed mathematical explanation of melting and solidification in phase change materials (PCMs), modeled as moving boundary problems. The phase transition occurs in three stages: heating, absorption or release of latent heat at the interface, and heating after the transition. The classical Stefan model, which assumes heat transfer mainly by conduction and a constant temperature at the phase interface, forms the basic framework. The governing equations include one-dimensional heat conduction equations for both solid and liquid regions, linked by conditions that ensure temperature continuity and energy conservation at the interface. These yield the Stefan condition, which describes the movement of the phase boundary through the balance of conductive heat flow and latent heat transfer. Analytical solutions exist only for simpler cases, like the one-phase Stefan problem solved by the Neumann method. For more practical and complex situations, approximate methods—including the quasi-steady and Megerlin techniques—are introduced and compared for their accuracy over different Stefan numbers.