I will talk about the Baranov-Bessonov-Kapustin conjecture: "let θ be an inner function. Any bounded truncated Toeplitz operator on the model space Kθ admits a bounded symbol only if θ is a one-component inner function." I will present all the objects involved: the model spaces, the one-component inner functions and finally the truncated Toeplitz operators. Eventually, if there is enough time, I will present a possible (in my opinion promising) approach to tackle this problem.