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Cascading outages can cause large blackouts, and a variety of methods are emerging to study this challenging topic. The Task Force on Understanding, Prediction, Mitigation, and Restoration of Cascading Failures, under the IEEE PES Computer Analytical Methods Subcommittee (CAMS), seeks to consolidate and review the progress of the field towards methods and tools of assessing the risk of cascading failure. This paper discusses the challenges of cascading failure and summarizes a variety of state-of-the-art analysis and simulation methods, including analyzing observed data, and simulations relying on various probabilistic, deterministic, approximate, and heuristic approaches. Limitations to the interpretation and application of analytical results are highlighted, and directions and challenges for future developments are discussed.