The resilience of electric power grids is threatened by natural hazards. Climate-related hazards are becoming more frequent and intense due to climate change. Statistical analyses clearly demonstrate a rise in the number of incidents (power failures) and their consequences in recent years. Therefore, it is of utmost importance to understand and quantify the resilience of the infrastructure to external stressors, which is essential for developing efficient climate change adaptation strategies. To accomplish this, robust fragility and other vulnerability models are necessary. These models are employed to assess the level of asset damage and to quantify losses for given hazard intensity measures. In this context, a comprehensive literature review is carried out to shed light on existing fragility models specific to the transmission network, distribution network, and substations. The review is organized into three main sections: damage assessment, fragility curves, and recommendations for climate change adaptation. The first section provides a comprehensive review of past incidents, their causes, and failure modes. The second section reviews analytical and empirical fragility models, emphasizing the need for further research on compound and non-compound hazards, especially windstorms, floods, lightning, and wildfires. Finally, the third section examines risk mitigation and adaptation strategies in the context of climate change. This review aims to improve the understanding of approaches to enhance the resilience of power grid assets in the face of climate change. These insights are valuable to various stakeholders, including risk analysts and policymakers, who are involved in risk modeling and developing adaptation strategies.