The paper discusses the robustness of interdependent networks, where nodes in one network depend on nodes in another. It reviews analytical frameworks for studying percolation in such systems, which is crucial for understanding how failures propagate through interconnected infrastructures. The study highlights that interdependent networks can exhibit different phase transitions compared to isolated networks, with cascading failures leading to catastrophic outcomes. The framework developed uses generating functions to model the dynamics of cascading failures and derive steady-state solutions. It shows that the critical percolation threshold depends on the structure and dependencies between networks. The paper also presents several examples of interdependent networks, including tree-like, loop-like, and random regular networks, and demonstrates how their robustness changes with network parameters. It emphasizes the importance of understanding interdependencies in real-world systems, such as transportation, biological, and economic networks, to design more resilient infrastructures. The study concludes that the robustness of interdependent networks is influenced by factors such as the degree distribution, the number of interdependent nodes, and the presence of feedback loops. It also suggests that future research should focus on real-world applications and the development of theoretical tools to account for correlations in network structures.The paper discusses the robustness of interdependent networks, where nodes in one network depend on nodes in another. It reviews analytical frameworks for studying percolation in such systems, which is crucial for understanding how failures propagate through interconnected infrastructures. The study highlights that interdependent networks can exhibit different phase transitions compared to isolated networks, with cascading failures leading to catastrophic outcomes. The framework developed uses generating functions to model the dynamics of cascading failures and derive steady-state solutions. It shows that the critical percolation threshold depends on the structure and dependencies between networks. The paper also presents several examples of interdependent networks, including tree-like, loop-like, and random regular networks, and demonstrates how their robustness changes with network parameters. It emphasizes the importance of understanding interdependencies in real-world systems, such as transportation, biological, and economic networks, to design more resilient infrastructures. The study concludes that the robustness of interdependent networks is influenced by factors such as the degree distribution, the number of interdependent nodes, and the presence of feedback loops. It also suggests that future research should focus on real-world applications and the development of theoretical tools to account for correlations in network structures.