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Extreme climatic events have significant impacts on society and the environment, especially when multiple hazards occur concurrently (e.g., drought and heat waves) or consecutively (wildfires and extreme precipitation). A large number of indicators have been developed to detect and study changes in extreme events across space and time. While the current climate extreme indicators provide useful information, most do not provide any information on compound/concurrent events. A compound event corresponds to a situation in which multiple (often interrelated) hazard drivers lead to an extreme outcome. Therefore, current univariate methods used for frequency analysis and risk assessment may underestimate the risk or occurrence probability of extreme events. After a comprehensive review of the existing methods, this study outlines frameworks for detecting, modeling, and analyzing inter-related events and processes including compound extremes.