Over the years, power systems have been severely affected by extreme events. This situation has worsened given that climate change has proven to exacerbate their frequency and magnitude. In this context, resilience assessments have proved crucial to prevent and tackle the effects of these events on power systems. Some resilience studies have taken advantage of the so-called fragility curves (FCs) to evaluate the vulnerability of the system components against these natural hazards. Conceptually, FCs provide the failure probability of a particular grid asset according to the intensity of an extreme event, which can be determined based on the hazard intensity inherently dictated by the nature of the event. The probability of failure can be obtained following diverse methodologies and criteria. Thus, the resilience assessment of the event may vary significantly depending on how the probability of failure was determined. This paper provides, for the first time, a comprehensive review of the FCs used to model the vulnerability of the power system components, classifying them according to the physical magnitude and the system element subject to each type of event. Furthermore, a comparison of results obtained applying different FCs is developed to show the relevance of their modelling. The content of this paper can be used as a hands-on guide for researchers and power systems engineers to perform resilience studies.