With great enthusiasm we present this special issue of Journal of Physics D: Applied Physics, which collects the best selection of the recent state-of-the-art in experimental and numerical research of non-thermal plasma sources and discharge regimes and their wide application possibilities. The research achievements and generation of such plasma discharges promote the advances in many areas of science and technology and open or stimulate new horizons and possibilities for their uses. The issue presents a wide spectrum of new approaches for pulsed generation of plasmas by the ultra-high electric field of nanosecond/ sub-nanosecond duration, formation of discharges with runaway electrons, and generation of plasma by electromagnetic beams from microwave to terahertz diapason. New plasma regimes that were created by various plasma jets and multi-jets, dielectric barrier or other kinds of gas discharges operating in gases, as well as discharges interacting with or directly in liquids are also extensively addressed. Several contributions include modeling of some of these new plasma regimes, and most of them provide examples of applications that benefit from these plasma source designs, with a special focus on biomedical, agricultural, combustion, environmental, nanoparticle and diamond synthesis, and other emerging applications. The special issue is launched with a topical review on low pressure discharges with hollow cathode and anode and their applications, by Korolev and Koval [1]. As historically plasma science started with low pressure electrical discharges and recently the focus moved to atmospheric pressure with a large variety of new applications, reviewing low pressure discharges with extremely small neutral particle density and electron free path in excess of the size of the discharge gap, where the discharge regimes are between the avalanche ioniz ation and pure vacuum discharge in the cathode metal vapors, is still timely. New approaches to the interpretation of the discharge formation mechanism and sustaining are discussed and offer the possibility 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. Several research papers in the issue deal with recent developments and new plasma regimes under low pressures. Burdovitsin et al [2] investigated the beam-plasma formed by an energetic electron beam at fore-vacuum pressure (1-10 Pa range). The maximum plasma density at the optimum collector potential can be much greater than the plasma density when the collector is at ground or at floating potential. Bokhan et al [3] studied an open discharge with counter-propagating electron beams applicable in high voltage pulsed switches with a sub-nanosecond leading edge (kivotrons). It was shown that a fast current development arises when the discharge self-sustaining mode is caused by the photoemission from the cathodes due to the resonant radiation emitted by fast helium atoms with a...