The damage and fracture of materials are technologically of enormous interest due to their economic and human cost. They cover a wide range of phenomena like e.g. cracking of glass, aging of concrete, the failure of fiber networks in the formation of paper and the breaking of a metal bar subject to an external load. Failure of composite systems is of utmost importance in naval, aeronautics and space industry. By the term composite, we refer to materials with heterogeneous microscopic structures and also to assemblages of macroscopic elements forming a super-structure. Chemical and nuclear plants suffer from cracking due to corrosion either of chemical or radioactive origin, aided by thermal and/or mechanical stress. Despite the large amount of experimental data and the considerable effort that has been undertaken by material scientists, many questions about fracture have not been answered yet. There is no comprehensive understanding of rupture phenomena but only a partial classification in restricted and relatively simple situations. This lack of fundamental understanding is indeed reflected in the absence of reliable prediction methods for rupture, based on a suitable monitoring of the stressed system. Not only is there a lack of non-empirical understanding of the reliability of a system, but also the empirical laws themselves have often limited value. The difficulties stem from the complex interplay between heterogeneities and modes of damage and the possible existence of a hierarchy of characteristic scales (static and dynamic). The paper presents a review of recent efforts from the statistical physics community to address these points.
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