This manuscript reviews published works related to plasma assistance in supersonic combustion / focusing on mixing enhancement, ignition and flameholding. A special attention is paid for studies, which the author participated in person. The Introduction discusses general trends in plasma-assisted combustion and, specifically, work involving supersonic conditions. In Section 2, the emphasis is placed on different approaches to plasma application for fuel ignition and flame stabilization. Several schemes of plasma-based actuators for supersonic combustion have been tested for flameholding purposes at flow conditions where self-ignition of the fuel/air mixture is not realizable due to low air temperatures. Comparing schemes indicates an obvious benefit of plasma generation in-situ, in the mixing layer of air and fuel. In Section 3, the problem of mixing enhancement using a plasma-based technique is considered. The mechanisms of interaction are discussed from the viewpoint of triggering gasdynamic instabilities promoting the kinematic stretching of the fuel-air interface. Section 4 is related to the description of transitional processes and combustion instabilities observed in plasma-assisted high-speed combustion. The dynamics of ignition and flame extinction are explored. It is shown that the characteristic time for reignition can be as short as 10 ms. Two types of flame instability were described which are related to the evolution of a separation zone and thermoacoustic oscillations, with characteristic times 10 ms and 1 ms correspondingly.