Robust interconnections have been the subject of study by the control community for several decades. Substantial progress has been made in the context of both stability and performance robustness for various types of interconnections. Typical problems addressed in the literature involved interconnections with simple topologies but with more complex components (dynamic, sometimes with high dimensions). More recently, the attention of the research community shifted towards networked systems where the topology of the network is fairly large and complicated while the local dynamics are fairly simple. The term fragility is used in this context to highlight the system’s closeness to failure. Notions of failure include large amplification of local disturbances (or shocks), instability, or a substantial increase in the probability of extreme events. Cascaded failure or systemic risk fits under this umbrella as well and focuses on local failures synchronizing to cause a break down in the network. Many abstracted models from transportation, finance, or the power grid fit this framework well. The focus of research is to relate fragility to the size and characteristics of a network for certain types of local interactions. In this talk, I will discuss commonality between robustness (or the lack of) and fragility and show how classical techniques from control theory coupled with graph theory provide answers to some interesting classes of problems. I will present some examples to illustrate these connections..