The ignition and the stable combustion provide two critical points in the combustion studies and applications. With the plasma actuation, not only the gas flow is heated, but also a large quantities of chemical substances are produced by the non-equilibrium plasma, such as the excited molecules and free radicals, which could be used to realize a wide range of ignition, to reduce the ignition delay, to improve the stability of the flame and to expand flammable limits together with other advantages. A great amount of experiments and numerical simulations were carried out in Russia. This paper reviews the data available and discusses their treatments. Some conclusions on the main achievements and prospects of the future investigations in this field are made. The results definitely confirm that the field of the plasma ignition and the plasma-assisted combustion is highly promising for a number of industrial applications.