The effect of increased populations concentrated in urban areas, coupled with the ongoing threat of climate change, means that society is becoming increasingly vulnerable to the effects of extreme precipitation. The study of these events is therefore a key topic in climate research, in their physical basis, in the study of their impacts, and in our adaptation to them. From a meteorological perspective, the main questions are related to the definition of extreme events, changes in their distribution and intensity both globally and regionally, the dependence on large‐scale phenomena including the role of moisture transport, and changes in their behavior due to anthropogenic pressures. In this review article, we address all these points and propose a set of challenges for future research. This article is categorized under: Science of Water > Water Extremes Science of Water > Hydrological Processes Main oceanic and terrestrial moisture sources and their area of higher moisture contribution are associated with extreme precipitation events. The rounded areas represent the regions where the source of higher contribution changed compared with climatological mean precipitation. The sources defined are North and South Atlantic Ocean (NATL and SATL), North and South Pacific Ocean (NPAC and SPAC), Mediterranean and Red Seas (MED and REDS), Gulf of Mexico (MEXCAR), Indian Ocean and Zanzibar Current and Arabian Sea (IND and ZANAR), Agulhas Current (AGU), South America (SAM), Sahel Region (SAHEL), and South Africa (SAFR).