In recent decades particular interest in applications of nonequilibrium plasma for the problems of plasma-assisted ignition and plasma-assisted combustion has been observed. A great amount of experimental data has been accumulated during this period which provided the grounds for using low temperature plasma of nonequilibrium gas discharges for a number of applications at conditions of high speed flows and also at conditions similar to automotive engines. The paper is aimed at reviewing the data obtained and discusses their treatment. Basic possibilities of low temperature plasma to ignite gas mixtures are evaluated and historical references highlighting pioneering works in the area are presented. The first part of the review discusses plasmas applied to plasma-assisted ignition and combustion. The paper pays special attention to experimental and theoretical analysis of some plasma parameters, such as reduced electric field, electron density and energy branching for different gas discharges. Streamers, pulsed nanosecond discharges, dielectric barrier discharges, radio frequency discharges and atmospheric pressure glow discharges are considered. The second part depicts applications of discharges to reduce the ignition delay time of combustible mixtures, to ignite transonic and supersonic flows, to intensify ignition and to sustain combustion of lean mixtures. The results obtained by different authors are cited, and ways of numerical modelling are discussed. Finally, the paper draws some conclusions on the main achievements and prospects of future investigations in the field.