Creating novel interpretations of existing musical compositions is and has always been an essential part of musical practice. Before the advent of recorded music, listening to a piece of music mostly meant listening to a version of it, in many cases, performed by musicians other than the original composer or performer. While this practice, along with musical notation, allows compositions to remain known for many decades or even centuries, it also provides room for artistic expression. Oftentimes, versions that are reproduced faithfully with respect to the original composition are seen as tributes to honor the composers; however, versions that are altered with the limitless creativity of humans often demonstrate how an existing idea can be transformed into something that goes beyond the original intention. Regardless of the ways in which musical versions are created, they are fundamental to the world's musical heritage.In this article, we consider a musical version to be "any rendition or performance of an existing musical composition." Another widely used term in the literature is "cover songs"; however, there are three main reasons we avoid using that term in this article. Firstly, the scope of the term is not clear as many authors limit its use to certain genres (e.g., pop and rock) and time periods (e.g., after the 1950s). Secondly, it has negative historical and economic connotations that date back to when the term emerged: record labels often asked White musicians to record (or cover) the songs of Black musicians as a marketing strategy to reach certain demographics. Lastly, the term does not represent the wide range of musical versions that are the subject of this article (see Fig. 1). Therefore, we employ the term "musical versions" throughout this article for being as inclusive as possible.This survey article focuses on the literature studying musical version identification and retrieval from a computational perspective. A key concept we refer to throughout this article is the concept of similarity, which we aim to quantify and model in a way that would reflect musical versions as semantically closer than non-versions. Following the literature, we consider that all versions of the same composition belong to the same group, or clique.