In the course of this thesis, solid-liquid phase transformations in metallurgical slag systems are investigated. A thermodynamic software package is developed that can be used together with a thermodynamic database to calculate thermochemical equilibrium conditions and simulate the kinetics of solid-liquid phase transformations in multi-component, multi-phase systems. In order to gain a better understanding of the rate-determining processes, key experiments using High-Temperature Confocal Scanning Laser Microscopy (HT-CSLM) are performed. The experimental observations are complemented and interpreted by numerical modelling. The dissolution kinetics of various oxide particles in multi-component slags is predicted for the case that the interdiffusivity matrix is known. The combination of thermodynamic modelling and key experiments reveals the physical processes limiting the kinetics of the solid/liquid phase transformations. The kinetics of the dissolution of solid particles in multi-component slags appears to be diffusion controlled, where convection is considered by a decreased boundary layer thickness.