Reliability management is of great importance for the secure and sufficient operation of power systems, thus the n — KG — KL contingency constrained unit commitment (CCUC) problem is determined for investigation in this paper. In order to reveal the capability of different methods on the solution of CCUC, both explicit and implicit decomposition frameworks have been investigated, as well as their inner feedback strategies, such as Benders decomposition and column-and-constraint generation (CCG) algorithm. In addition, sensitivity analysis, multi-cut strategy, and parallel implementation have also been analyzed and discussed. The comparison between nine explicit and implicit methods — all of them are deterministic with different configurations and the global optimal can be guaranteed in a finite number of iterations — is carried out on the IEEE 24-bus system, resulting in several interesting conclusions. Finally, the IEEE 118-bus test system is employed to explore the potential on the large-scale instance.