There is an increasing number of studies focusing on extreme weather all over the world, but global trends and research topics related to extreme weather are still unclear. This study aimed to explore the current situation, research themes, and future trends in the field of extreme weather. Publications published from 1980 to 2019 were identified and retrieved from the Web of Science Core Collection databases by using keywords on May 5, 2020. Excel 2019, VOSviewer, R, and CiteSpace were used for scientific analysis. The results showed that (1) the number of publications on extreme weather research has rapidly increased and expanded continually, shifting from core disciplines to interdisciplinary fields; (2) the International Journal of Climatology was the most productive journal, and climate and environment were the most popular subject categories. Most studies were carried out in the USA, China, Germany, and other nations, and the Chinese Academy of Sciences was the most productive institution; (3) the main research topics were summarized as (a) climate change; (b) variability; (c) trends; (d) rainfall; (e) temperature; and (f) maximum. At the same time, (4) keyword bursts analysis showed that the domain focused on changes to atmospheric rivers, the impacts of global nitrogen content on extreme weather, and the relationship between water quality, soil moisture content, and extreme weather. Based on the in-depth analysis of extreme weather research, this paper developed a further understanding of the developments in this field over the past 39 years and also provided a reference for future research.