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Dance is an art and when technology meets this kind of art, it is a novel attempt in itself. Many researchers have attempted to automate several aspects of dance, right from dance notation to choreography; from dance capturing to dance generation. We define and illustrate the concept of ‘Dance Automation’ in this paper. Furthermore, we have encountered several applications of dance automation like e-learning, heritage preservation, medical therapy, etc. Despite decades of continuous attempts by many researchers in various styles of dance all round the world, we found a review paper that portrays the research status in this area of ‘dance and computers’ dating to 1990 (Leonardo 1990 Computers and dance: A bibliography, pp. 87–90). Hence, we decided to compose a comprehensive review article that showcases several aspects of dance automation and document contributions of researchers in marrying creativity with logic. This paper is an attempt to review research work reported in the literature, categorize and group significant research work completed in a span of 1967–2020 in the field of automating dance. We have explicitly identified six major categories corresponding to the use of computers in dance automation, namely, dance representation, dance capturing, dance semantics, dance generation, dance processing approaches and applications of dance automation systems. We classified several research papers under these categories according to their research approach and functionality. With the help of proposed categories and subcategories, one can easily determine the state of research and the new avenues left for exploration in the field of dance automation.