In recent years, the addition of the slag phase to numerical models of the Continuous Casting (CC) process has opened the door to a whole new range of predictions. These include the estimation of slag infiltration and powder consumption (lubrication), heat transfer and cooling through the cooper mould (solidification) and investigating the effect of operational parameters such as mould oscillation and powder composition on surface quality / defect formation. This work presents 2D and 3D CC models capable of describing the dynamic behaviour of the liquid/solid slag in both the shell mould-gap and bed as well as its effects on heat extraction and shell formation. The present paper also illustrates the application of the model to a variety of casters and the challenges faced during its implementation. The model attained good agreement on the prediction of mould temperatures and shell thicknesses as well as slag film formation and heat flux variations during the casting sequence. The effect of different oscillation strategies (sinusoidal and non-sinusoidal) was explored in order to enhance powder consumption and surface quality. Furthermore, the modelling approach allows one to predict the conditions leading to irregular shell growth and uneven lubrication; these are responsible for defects such as, stickers, cracking and, in the worst case scenario, to breakouts. Possible mechanisms for defect formation are presented together with strategies to enhance process stability and productivity of the CC machine.