Study of neutrino oscillations in long-baseline accelerator experiments

A review of the title subject is given. The phenomenology of neutrino oscillations in the framework of the so-called neutrino Standard Model ($\nu$SM) with three active neutrinos is considered. The recently completed long-baseline accelerator experiment K2K and currently in-progress MINOS and OPERA experiments are described in detail. The oscillation parameters obtained from the global analysis of all oscillation data are given. The short-baseline experiment MiniBooNE and its results on the search for light sterile neutrinos are discussed in detail. Considerable attention is given to searching for $\nu_{\mu} \to \nu_{e}$ oscillations and measuring the $\theta_{13}$ angle in muon neutrino experiments. The concept of the off-axis neutrino beam is reviewed. The T2K experiment, collecting statistics since early 2010, is described for its details and objectives. The NO$\nu$A experiment under construction and the next-generation beta beam and neutrino factory experiments are also discussed.