Cluster algebras capture a remarkable pattern relating different coordinate systems on special spaces such as spaces of matrices, spaces of continuous symmetries, and spaces of hyperbolic metrics. Since their introduction in 2001, this phenomenon has been discovered in a staggering cross section of mathematical contexts. Only recently, an explanation of this phenomenon emerged via ideas coming from mirror symmetry. In this talk, I will give a tour of the history of cluster algebras, from their origins in canonical bases to the horizons of theta functions.