The review relates to low-pressure discharges with a hollow cathode and a hollow anode. The term ‘low pressure’ implies that a neutral particle density is extremely small and the electron free path for ionization is in excess of the characteristic size for the discharge gap. On the other hand, the neutral particles still play an essential role in forming the gas-discharge plasma. Thus, the discharge regimes keep an intermediate position between the classical low-pressure discharge with avalanche ionization and pure vacuum discharge that burns in the cathode metal vapor. New approaches to the interpretation of the discharge formation mechanism at the stage of delay time to breakdown, and for the discharge sustaining features at the later temporal stages, are discussed. The developed approaches offer the possibility of interpreting the discharge behavior in the systems to obtain a uniform plasma in a large volume of the cathode or anode cavity, in the sources of electron and ion beams based on the plasma cathode and in the high-current pseudospark switches.