The Boltzmann-Gibbs-von Neumann-Shannon (BG) entropic functional is additive, which is at the basis of its well-known centennial success. Indeed, the celebrated BG statistical mechanics is grounded on this simple entropic property. However, although sufficient, it is not necessary for the validity of (properly scaled) classical thermodynamics and its associated Legendre-transform structure. We shall argue about the need of nonadditive entropic functionals for discussing a plethora of equilibrium and nonequilibrium phenomena in wide classes of natural, artificial, and social complex systems. Selected illustrations will be briefly presented. Bibliography available at https://tsallis.cbpf.br/biblio.htm