In this talk I report on joint work with Patrick Gérard concerning the construction of global Birkhoff coordinates for the Benjamin-Ono equation. In these coordinates this equation can be solved by quadrature, meaning that it is an integrable (pseudo)differential equation in the strongest possible sense. The construction is based on the Lax pair formulation of this equation. I will present spectral properties of the Lax operator, discuss a generating function of the Benjamin-Ono hierarchy, which allows to establish various trace formulas, and introduce the Birkhoff coordinates. Furthermore, I will provide a characterization of finite gap solutions.