A review is presented of theoretical concepts of properties of matter and of processes in neutron star shells and of their relation to observations. The formation of a hot neutron star and its subsequent cooling leads to the appearance of a nonequilibrium layer in which energy of up to 10$^{48}$ ergs is stored. The lack of equilibrium consists of the presence of superheavy nuclei with a large neutron excess near the limit of neutron evaporation $Q_n$ = 0 and of free neutrons. The slow diffusion of neutrons into the interior of the star maintains the x-ray luminosity $L_x\gtrsim$10$^{34}$ ergs/sec during $t\approx10^4$ years. Nonstationary processes are discussed which are associated with the existence of the nonequilibrium layer. Outward transport of nonequilibrium matter and nuclear explosions may be associated with the observed x-ray bursts. Breaking up of the crust accompanying the diffusion of neutrons into the interior of the star and the expansion of the shell may explain abrupt changes in the period of the Crab pulsar. Expulsion of neutrons and superheavy nuclei into interstellar space accompanying explosions and subsequent electrodynamic acceleration of particles may explain the origin of heavy elements with $A>$150 and also of deuterium.