This paper provides an overview of some of the recent developments in the assessment of network vulnerability and robustness through appropriate tools that assist in the quantification of network efficiency/performance and the identification of the importance of network components, such as nodes and links. We demonstrated how rigorously constructed and well-defined network measures can capture not only the network topology underlying a particular critical system, but also the underlying behavior of decision-makers, the resulting flows, and induced costs in the reality of demands for resources, whether fixed or elastic (price-dependent). In addition, we reviewed how to determine the synergy associated with network integration, with a focus on supply chains, as may occur not only in corporate applications, such as in mergers and acquisitions, but also in humanitarian ones, as in the case of the creation of teams and partnerships for humanitarian logistics. We illustrated the concepts and tools in this paper, which are based on numerous publications, through a spectrum of applications and numerical examples. Because the number of disasters is growing globally, it is imperative to have transparent, well-understood, and appropriate tools for the determination of network vulnerability and robustness, as critical infrastructure networks from transportation, telecommunications, supply chains, to financial and electric power ones, provide the ties that bind our economies and societies together. Local disruptions can have global impacts. Only when network components are identified as to their importance and rankings can decision-makers and policy analysts, as well as planners and engineers, understand in an objective way which components should be maintained and protected the most, with implications for disaster and emergency preparedness as well as national security.