With the main objective that it can be consulted by all researchers, mainly young people, interested in the study of the Kac-Moody algebras and their applications, this paper aims to present the past and present state-of-the-art developments and results on these algebras at various levels of analysis and fields of application in different disciplines. Indeed, lot of references in the literature on these algebras are analyzed and a study of the most relevant topics regarding them is shown