Biomaterials and biosystems often display enhanced fault tolerance, being able to maintain certain performance levels in spite of accumulated damage. This resilient behaviour is often related to the resilience of the network structure that describes the system’s components and their mutual interactions. I will review basic concepts of network resilience, highlighting the pitfalls of current approaches, which require unrealistic system sizes in order to justify the fault tolerance of real systems. I will discuss an alternative definition of resilience, inspired by the hierarchical structure of biosystems. Finally, I will show how such concepts can be transferred to fracture modeling in biomaterials.