Power grids are cyber-physical systems and can be modelled as network systems where individual units (generators, busbars and loads) are interconnected through physical and cyber links. Network components (nodes/edges) may undergo intentional and/or random failures. In catastrophic cases, a failure initiating from a small set of these components can quickly propagate through the whole network, leading to a cascade of failures that might force a deep whole-grid blackout. Often network components have different vitality and protecting some is more critical than others. This manuscript aims to provide a focused overview of modelling power grids as complex networks and their resilience and reliability analysis. We also perform a critical review of vitality metrics and their precision in power grid resilience analysis. The review is accompanied by some simulations on benchmark and real power grids to show the applicability of these concepts in studying resilience.