  Predicting when rupture occurs or cracks progress is a major challenge in
numerous elds of industrial, societal and geophysical importance. It remains
largely unsolved: Stress enhancement at cracks and defects, indeed, makes the
macroscale dynamics extremely sensitive to the microscale material disorder.
This results in giant statistical uctuations and non-trivial behaviors upon
upscaling dicult to assess via the continuum approaches of engineering. These
issues are examined here. We will see: How linear elastic fracture mechanics
sidetracks the diculty by reducing the problem to that of the propagation of a
single crack in an eective material free of defects, How slow cracks sometimes
display jerky dynamics, with sudden violent events incompatible with the
previous approach, and how some paradigms of statistical physics can explain
it, How abnormally fast cracks sometimes emerge due to the formation of
microcracks at very small scales.
