Three-Flavor 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 θ13 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 NOνA . We discuss in detail the role of accelerator neutrino experiments in the precision era of neutrino physics in view of DUNE and Hyper-Kamiokande, the program of systematic uncertainty reduction and the development of new beam facilities.