Abstract This paper presents an overview of experimental and numerical investigations of the nonequilibrium cold plasma generated under high overvoltage and further usage of this plasma for plasma-assisted combustion. Here, two different types of the discharge are considered: a streamer under high pressure and the so-called fast ionization wave (FIW) at low pressure. The comprehensive experimental investigation of the processes of alkane slow oxidation in mixtures with oxygen and air under nanosecond uniform discharge has been performed. The kinetics of alkane oxidation has been measured from methane to decane in stoichiometric and lean mixtures with oxygen and air at room temperature under the action of high-voltage nanosecond uniform discharge. The efficiency of nanosecond discharges as active particles generator for plasma-assisted combustion and ignition has been investigated. The study of nanosecond barrier discharge influence on a flame propagation and flame blow-off velocity has been carried out. With energy input negligible in comparison with the burner's chemical power, a double flame blow-off velocity increase has been obtained. A signicant shift of the ignition delay time in comparison with the autoignition has been registered for all mixtures. Detonation initiating by high-voltage gas discharge has been demonstrated. The energy deposition in the discharge ranged from 70 mJ to 12 J. The ignition delay time, the velocity of the flame front propagation, and the electrical characteristics of the discharge have been measured during the experiments. Under the conditions of the experiment, three modes of the flame front propagation have been observed, i.e., deflagration, transient detonation, and Chapman-Jouguet detonation. The efficiency of the pulsed nanosecond discharge to deflagration-to-detonation transition (DDT) control has been shown to be very high.