Three-flavour oscillations with accelerator neutrino beams

The three-flavor neutrino oscillation paradigm is well established in particle physics thanks to the crucial contribution of accelerator neutrino beam experiments. In this paper we review the most important contributions of these experiments to the physics of massive neutrinos after the discovery of $\theta_{13}$ and future perspectives in such a lively field of research. Special emphasis is given to the technical challenges of high power beams and the oscillation results of T2K, OPERA, ICARUS and NO$\nu$A. We discuss in details the role of accelerator neutrino experiments in the precision era of neutrino physics in view of DUNE and Hyper-Kamiokande, the programme of systematic uncertainty reduction and the development of new beam facilities.