Robust biological signaling networks evolved, through gene duplications, from simple, relatively fragile cascades. Architectural features such as layered configuration, branching and modularity, as well as functional characteristics (e.g., feedback control circuits), enable fail-safe performance in the face of internal and external perturbations. These universal features are exemplified here using the receptor tyrosine kinase (RTK) family. The RTK module is richly mutated and overexpressed in human malignancies, and pharmaceutical interception of its signaling effectively retards growth of specific tumors. Therapy-induced interception of RTK-signaling pathways and the common evolvement of drug resistance are respectively considered here as manifestations of fragility and plasticity of robust networks. The systems perspective we present views pathologies as hijackers of biological robustness and offers ways for identifying fragile hubs, as well as strategies to overcome drug resistance.