I investigated failure phenomena emerging in complex systems which are composed of a large number of interacting elements. My research was focused in two main directions: First, I tried to obtain a deeper understanding of the phase transition analogy of fracture processes. For this purpose I studied how a solid body perforates due to dynamic impact loading as the energy of impact is varied at different amounts of materials’ disorder. As the next step, I focused on the cascading failure mechanism driven by load redistribution on complex networks with the aim to understand how the interplay of the topology of the network of load transmitting connections and the disordered local strength affects the statistical and dynamical features of failure cascades. I used the approaches and tools of statistical physics, phase transitions and critical phenomena, the physics of complex systems, and network science