The paper provides a comprehensive overview of Mittag-Leffler functions and their applications. The authors, H.J. Haubold, A.M. Mathai, and R.K. Saxena, present a detailed account of the Mittag-Leffler function, generalized Mittag-Leffler functions, and their properties. The Mittag-Leffler function, defined as \( E_{\alpha}(z) = \sum_{k=0}^{\infty} \frac{z^k}{\Gamma(1+\alpha k)} \), has been widely used in various fields of science and engineering due to its potential in solving problems related to fractional calculus, complex systems, and non-linear dynamics. The paper covers special cases, functional relations, basic properties, recurrence relations, asymptotic expansions, integral representations, and connections with fractional calculus operators. It also discusses the generalized Mittag-Leffler functions and their applications in solving fractional differential equations and boundary value problems. The authors provide a list of references to highlight the current trends in research on Mittag-Leffler functions and their applications.The paper provides a comprehensive overview of Mittag-Leffler functions and their applications. The authors, H.J. Haubold, A.M. Mathai, and R.K. Saxena, present a detailed account of the Mittag-Leffler function, generalized Mittag-Leffler functions, and their properties. The Mittag-Leffler function, defined as \( E_{\alpha}(z) = \sum_{k=0}^{\infty} \frac{z^k}{\Gamma(1+\alpha k)} \), has been widely used in various fields of science and engineering due to its potential in solving problems related to fractional calculus, complex systems, and non-linear dynamics. The paper covers special cases, functional relations, basic properties, recurrence relations, asymptotic expansions, integral representations, and connections with fractional calculus operators. It also discusses the generalized Mittag-Leffler functions and their applications in solving fractional differential equations and boundary value problems. The authors provide a list of references to highlight the current trends in research on Mittag-Leffler functions and their applications.