The analysis of network robustness tackles the problem of studying how a complex network behaves under adverse scenarios, such as failures or attacks. In particular, the analysis of interdependent networks’ robustness focuses on the specific case of the robustness of interacting networks and their emerging behaviors. This survey systematically reviews literature of frameworks that analyze the robustness of interdependent networks published between 2005 and 2017. This review shows that there exists a broad range of interdependent network models, robustness metrics, and studies that can be used to understand the behaviour of different systems under failure or attack. Regarding models, we found that there is a focus on systems where a node in one layer interacts with exactly one node at another layer. In studies, we observed a focus on the network percolation. While among the metrics, we observed a focus on measures that count network elements. Finally, for the networks used to test the frameworks, we found that the focus was on synthetic models, rather than analysis of real network systems. This review suggests opportunities in network research, such as the study of robustness on interdependent networks with multiple interactions and/or spatially embedded networks, and the use of interdependent network models in realistic network scenarios.