Large blackouts with significant societal and economic impacts result from cascade of failures in the transmission network of power grids. Understanding and mitigating cascading failures in power grids is challenging due to the large number of components and their complex interactions, wherein, in addition to the physical topology of the system, the physics of power flow and functional dependencies among components largely affect the spatial distribution and propagation of failures. In this dissertation, data-driven interaction graphs, which help in capturing the underlying interactions and influences among the components during cascading failures, are used for capturing the non-local nature of propagation of failures as well as for simplifying the modeling and analysis of cascades. Particularly, influence and correlation graphs are constructed for revealing and comparing various types of interactions/influences during cascades. In addition, as a step towards analyzing cascades, community structures in the interaction graphs, which bear critical information about cascade processes and the role of system components during cascades are identified. The key idea behind using community structures for analyzing cascades is that a cascade entering a community is likely to reach to most of the other members of the same community while less likely to reach to other communities. Thus, community structures significantly impact cascade behavior by trapping failures within communities. Further, a centrality measure based on the community structures is proposed to identify critical components of the system, which their protection can help in containing failures within a community and prevent the propagation of failures to large sections of the power grid. Various criticality evaluation techniques, including data-driven, epidemic simulation-based, power system simulation-based and graph-based, have been used to verify the importance of the identified critical components in the cascade process and compare them with those identified by traditional centrality measures. Moreover, it has been shown that the loading level of the power grid impacts the interaction graph and consequently, the community structure and criticality of the components in the cascade process. Furthermore, a Markov chain model is designed based on the community structures embedded in the data-driven interaction graphs of power grids. This model exploits the properties of community structures in interactions to enable the probabilistic analysis of cascade sizes in power grids. The trapping property of communities is extensively used to show that the probability distribution of cascade sizes exhibit power-law behavior as observed in previous studies and historical data. Finally, an integrated framework based on the influence model, a networked Markov chain framework, is proposed for modeling the integrated power grid and transportation infrastructures, through one source of their interdependency i.e., electric-vehicle (EV) charging stations. The interactions based on the rules and policies governing their internal and interaction dynamics is captured. Particularly, the proposed integrated framework is used to design an algorithm for assigning dynamic charging prices for the EV charging infrastructure with the goal of increasing the likelihood of having balanced charging and electric infrastructures. The proposed scheme for charging prices is traffic and power aware as the states and interactions of transportation and power infrastructures are captured in the integrated framework. Finally, the critical role of cyber infrastructure in enabling such collaborative solutions is also discussed.