The machining of brittle materials ranging from ceramics and glasses to composites such as ceramic matrix composites is already an established part of the process chain in branches of industry such as aerospace, automotive and medical engineering. Compared to ductile materials such as metals, the key challenge in machining brittle materials is the rapid and sometimes seemingly random propagation and expansion of cracks in the material as early as the initial contact between tool and material. This behaviour extends throughout the entire machining process. The associated damage and machining mechanisms are not well understood, especially for complex brittle composites such as CMCs. Numerical simulations of the machining process offer the potential to study and improve the understanding of the underlying mechanisms. For CMC, the complexity of the anisotropic material structure with brittle-hard materials represents a crucial difficulty. In the context of this presentation, approaches for modelling and simulating ceramic matrix composites for the machining process will be introduced and the state of the art from different areas of machining such as ceramics and carbon fibre reinforced plastics will be consulted.