The two simplest axisymmetric systems (multi-mirror and gas dynamic) for plasma heating and confinement are described. Significant progress in understanding the key physical phenomena in heating and confinement of plasma made it possible to suppress longitudinal electron thermal conductivity (by three orders of magnitude, in the case of the multi-mirror system), to stabilize MHD instabilities in axisymmetric geometry. As a result of such suppression, in the case of the multi-mirror trap, a dense plasma (ne ∼ 1021 m−3) was heated up to Te ≈ Ti ≈ 2 keV or even higher. Until now no limitations preventing further growth of plasma parameters have been observed. The main goal of the gas dynamic trap studies is a demonstration of the feasibility of a 14 MeV neutron source (NS) with a neutron flux density of 2 MW m−2, and a testing zone area of 1 m2 for structural tests of fusion materials. In this paper, the most important results on the MHD stability of plasma in axisymmetric geometry, as well as the formation of fast sloshing ions population and the D–D neutrons generation are presented. Currently, the upgrade of the GDT device has been completed. We also report on the construction of new neutral beam injectors with total power of up to 10 MW and heating pulse duration of 5 ms (corresponding to a steady state regime). According to calculations, the feasibility of a 'moderate' NS with a neutron flux of 0.5 MW m−2 can be demonstrated with the new neutral beam injection system in the near future. Preliminary experiments with the first two new NB injectors are currently being carried out at the Budker Institute of Nuclear Physics.