In this talk we introduce a new notion called the quantum wreath product that produces an algebra from a given algebra and a choice of parameters. Important examples include many variants of the Hecke algebras, such as (1) the cyclotomic Hecke algebras, (2) the affine Hecke algebras and their degenerate version, (3) Wan-Wang’s wreath Hecke algebras, (4) Rosso-Savage’s (affine) Frobenius Hecke algebras, and (5) the Hu algebra which quantizes the wreath product between symmetric groups. Our uniform approach to both its structure and representation theory encompasses many known results which were proved in a case by case manner. I’ll also talk about an application regarding the Ginzburg-Guay-Opdam-Rouquier problem on quasi-hereditary covers of Hecke algebras. This is a joint work with Dan Nakano and Ziqing Xiang.