Connes' bicentralizer problem is one of the most famous open problems in the theory of type III factors. This conjecture was solved in the amenable case by Haagerup in 1984, hence completing Connes' work on the classification of amenable factors. But the general non-amenable case is still open to this day, 40 years after Haagerup's celebrated work. In this talk, I will first give an overview of Connes' bicentralizer problem, its history and motivations, then I will present some recent progress on this conjecture.