Recently, the use of machine learning (ML) in scientific disciplines has experienced an unprecedented increase. Finance has not been an exception. Several works have been published in recent years using mltechniques. However, one of the topics with the least number of developed papers is volatility in this context. Nevertheless, the data analyzed here suggest changes regarding this issue. Data obtained from the Web of Science database show that between 2001 and 2010 there were 33 published papers associated with this topic. Surprisingly, between 2019 and 2023, 189 manuscripts have been published related to this topic. The purpose of this work is to review the works related to the applications of ml in volatility. For this, a classification of the main proposals on this topic is proposed following a narrative methodology, accompanied by a statistical and bibliometric analysis in which novel techniques such as K-means were used. The results are suggestive. Although most papers focus on volatility prediction through neural networks and support vector machines, there is a lack of studies related to volatility transmission, calibration of volatility surfaces,and corporate finance. Moreover, the obtained results indicate that there is a gap in the production of worksrelated to these topics in finance and economics specialized journals.