Power grids deliver energy, and telecommunication networks transmit information. These two facilities are critical to human society. In this study, we conduct a comprehensive overview of the development of reliability metrics for power grids and telecommunication networks. The main purpose of this review is to promote and support the formulation of communication network reliability metrics with reference to the development of power grid reliability. We classify the metrics of power grid into the reliability of power distribution and generation/transmission and the metrics of telecommunication network into connectivity-based, performance-based, and state-based metrics. Then, we exhibit and discuss the difference between the situations of the reliability metrics of the two systems. To conclude this study, we conceive a few topics for future research and development for telecommunication network reliability metrics.