Abstract : Cluster algebras were discovered by Fomin and Zelevinsky in 2001. Since then, it has been shown that they are related to diverse areas of mathematics such as algebraic geometry, total positivity, quiver representations, string theory, statistical physics, non-commutative geometry, hyperbolic geometry, tropical geometry, KP solitons, discrete integrable systems, quantum mechanics, Lie theory, algebraic combinatorics, WKB analysis, and Poisson geometry.