abstract: During the nineties, M. Broué, G. Malle and R. Rouquier proposed a series of conjectures in order to generalize the classical setting of real reflection groups (Coxeter groups, Artin groups, Hecke algebras) to complex reflection groups. I will report on the state-of-art concerning these conjectures, including recent progress by G. Pfeiffer and myself on the one hand, by my student E. Chavli on the other hand.