Algebraic entropy was introduced by Bellon and Viallet as a measure of complexity of algebraic systems. Having zero algebraic entropy is one of the forms of integrability in discrete case. This talk will discuss how looking for algebraic entropy leads to interesting questions and answers in two settings: that of bipartite T-systems, coming from the world cluster algebras, and that of R-systems, coming from the recently active area of dynamical algebraic combinatorics. In the case of T-systems this leads to a classification result related to classifying all pairs of commuting Cartan matrices of affine type. The talk is based on joint works with Pavel Galashin.