This paper reviews recent statistical models for the failure of fibrous materials. The mathematical model is a chain-of-bundles model under assumptions relevant to the failure of single fibers, loose bundles of fibers, and fiber-matrix composites. In fatigue applications, the fibers are assumed to have a distribution for failure time which depends on the load history. Two types of load sharing rules are considered; the first redistributes the loads of failed fibers without geometric preference, and the second redistributes the loads locally. Fundamentally different behavior is revealed for the two types of rules. For analytical and numerical results that have been obtained, we discuss the implications. We also indicate the important versions of the problem that have not been solved, but conjecture aspects of the resulting behavior. Supporting evidence is discussed for these important conjectures.