This text records the Proceedings of the IUTAM Symposium held in Cardiff, UK in 2001. It contains 39 full-length and 16 short articles by established authorities and young outstanding researchers and addresses the analytical and computational aspects of the fracture of non-homogeneous materials as they are approached by specialists in mechanics, materials science and related fields. Despite the seemingly disparate nature of non-homogeneous materials addressed in the text ranging from rock, concrete, ceramics, composites on the one hand, and, polycrystals and metals with microinhomogeneities on the other, they have many common features. Thus, micromechanical modelling, macroscopic analysis and meso-scale lattice modelling that reveal underlying micromechanisms of fracture, and methods based on non-local and gradient theories have been given equal weight in the exposition. It will be useful to those active in research in fracture who wish to gain an up-to-date understanding of the subject from leading experts in the field.