Abstract <p>This review describes the current state of the art, methods, and techniques of neutron generation, as well as physical processes occurring in neutron tubes and compact (small-sized) neutron sources (and others axis-symmetrical devices) during their operation. The results of experimental and theoretical studies of deuteron acceleration in small-sized Penning sources, plasma ion diodes with magnetic isolation, generators based on plasma focus and laser influence, and neutron acceleration tubes of increased efficiency are presented.</p>