The representation theory of the symmetric group plays a central role in mathematics, particularly in combinatorics through its connection with symmetric functions. In this setting, the Iwahori–Hecke algebra can be viewed as a q-deformation of the group algebra of the symmetric group. Its representation theory depends on the parameter q, leading to different behavior for different values of q. In this talk, I focus on the case q = 0, namely the 0-Hecke algebra, whose representation theory is closely related to quasisymmetric functions. I will briefly review the history of this subject and discuss recent developments involving quasisymmetric functions and related combinatorics.