The high demand for smartphones and other devices incorporating flat-panel displays has given rise to substantial market potential for the processing of transparent dielectric materials (e.g. glass) using ultrashort pulse (USP) lasers. However, the current state of research as described in literature does not provide a full understanding of the ablation mechanisms involved, of beam propagation effects inside the glass volume, as well as of possible damage to the material from the laser process. Modelling and simulation techniques enable us to expand this understanding and identify ways of improving process speed and quality.