Failure and robustness in networks

We consider the physics of structural failure in complex systems and the ways in which we can guard against it, from the point of view of network theory. How, for instance, can we design a communication network to provide robust connections when nodes are expected to fail regularly? Conversely, given a network such as the social network of contacts over which a disease spreads, how can we attack it so as to make it fail and thereby prevent the spread of disease? We consider a variety of different definitions of failure and robustness, and discuss some of the interesting and sometimes paradoxical behaviors that can arise when networks fail.