We discuss experimental and theoretical achievements and problems connected
with studies of light halo nuclei during the last few years. In this talk
the discussion is limited to the case of one-nucleon halo systems: B-8, Be-
11 and C-19. Each of these nuclei has its own peculiarities and we consider
examples of recent experiments with radioactive beams of these nuclei at i
ntermediate and high energies. We discuss some of the developments of the t
heoretical understanding of one-nucleon halo nuclei. Special attention is p
aid to the problems which should be solved in the future.