Damage mechanics describes the progressive damage to a material under load, which leads to a reduction in strength and stiffness even before complete fracture occurs. Fracture mechanics investigates the behaviour of cracks and discontinuities in the material, in particular the propagation of cracks under mechanical stress until failure occurs. To describe this complex failure behaviour, damage models are developed that capture the relationship between material degradation, microstructure and load history. The phase-field method enables a detailed simulation of crack initiation, crack propagation and material failure.