Materials having a network of fibers as their main structural component abound in nature. Examples include the cytoskeleton, the extracellular matrix, connective tissue and many man-made materials such as paper and nonwovens. These are referred to collectively as network materials [1]. Rupture is a critical event in most applications involving such materials. However, damage accumulation and fracture in network materials is poorly understood. This talk reviews several results related to this topic including the failure modes and the relation between structure and strength and toughness. Rupture may develop by the accumulation of diffuse damage or by the propagation of a major crack (fracture mechanics type). The failure mode is controlled by a set of network structural parameters through a criterion which will be discussed. In the case of diffuse damage dominance, the strength and toughness may be also expressed in terms of non-dimensional groups of network and fiber/crosslinks parameters [2,3]. Toughness in this case is larger than in the case of rupture by the propagation of a major crack and is defined in terms of a new formulation of energy released per unit volume of material [4]. Standard (non-linear) fracture mechanics applies in the case of propagation of a major crack. However, network materials are strongly notch insensitive and the degree of notch insensitivity may be associated with the degree of non-affinity of the strain field [5]. Furthermore, fiber preferential orientation may lead to crack deflection, which becomes an important toughening mechanism in these materials [6].