Enhancing resiliency in a power grid system is one of the core mandates of electrical distribution companies to provide high-level service. The power resiliency research community has proposed numerous schemes, to detect, classify, and localize fault events. However, the literature still lacks a comprehensive taxonomy of these schemes which can help advance future research. This study aims to provide a compact yet comprehensive review of the state-of-the-art solutions to fault analysis in transmission power systems. We discuss fault types and several fault-analysis methodologies adopted by relevant research works, propose a novel framework to classify these works, and highlight their strengths and limitations. We anticipate that this brief review would be helpful as a literature review and benefit the research community in choosing suitable techniques for fault analysis.