Atmospheric Extreme Events (EEs) cause severe damages to human societies and ecosystems. The frequency and intensity of EEs and other associated events are increasing in the current climate change and global warming risk. The accurate prediction, characterization, and attribution of atmospheric EEs is therefore a key research field, in which many groups are currently working by applying different methodologies and computational tools. Machine Learning (ML) methods have arisen in the last years as powerful techniques to tackle many of the problems related to atmospheric EEs. This paper reviews the ML algorithms applied to the analysis, characterization, prediction, and attribution of the most important atmospheric EEs. A summary of the most used ML techniques in this area, and a comprehensive critical review of literature related to ML in EEs, are provided. A number of examples is discussed and perspectives and outlooks on the field are provided.This research has been partially supported by the European Union, through H2020 Project “CLIMATE INTELLIGENCE Extreme events detection, attribution and adaptation design using machine learning (CLINT)”, Ref: 101003876-CLINT. This research has also been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). J. Del Ser also acknowledges support by the Basque Government through EMAITEK and ELKARTEK funds (ref. KK-2020/00049), as well as the consolidated research group MATHMODE (IT1294-19)