This paper aims to provide quantitative statistics and a comprehensive review of the key influential and intellectual structure of asymmetric volatility and leverage effect in the stock market. This study reviews 271 articles and review papers published in scientific journals indexed by the Scopus database from 1994 to 2021. VOSviewer and Excel software are used to analyse the collected data and apply the bibliometric tests such as citation analysis of documents, source, authors, institutions and countries, Co-occurrence analysis of author keywords, co-authorship and Bibliographic coupling of authors, source and countries. By analysing the growth in this topic, during the first 10 years, the publication in this topic was considerably less. After that, until 2020, the growth is remarkable. Further, the study identifies the most influential and impactful authors, journals, institutions, and countries to asymmetric volatility and leverage effect in the stock market. To the best of the author’s knowledge, this is one of the first papers to address the literature of asymmetric volatility and leverage effect in the stock market from a bibliometric aspect. It helps researchers and other academicians to explore and build a quantitative base regarding the scientific development of asymmetric volatility and leverage effect in the stock market.