The use of plasmas in aerodynamics has become a recent topic of interest. The potentialities of different types of plasmas are being investigated for low velocity and high velocity flow control, as well as for plasma-assisted combustion. Dielectric barrier discharges (DBDs) are good candidates since the transition of the glow or filamentary discharge to an arc is prevented by the dielectric barrier. Moreover, surface DBDs allow to ionize the gas very close to the dielectric surface and can be used to ionize the boundary layer around an object immersed in a flow. The research in flow control has basically followed two main paths: the study of DBDs in low-speed airflows and the study of volume glow or corona discharges in supersonic airflows. Until today, there has been an important technological barrier in experimental investigations with surface DBDs. Atmospheric pressure surface DBDs in air have been difficult to maintain for long operation times, typically several hours, because reactive species created in the plasma (for example atomic oxygen) generate intensive etching of the electrode and dielectric materials. Oxidation of the electrodes or reduction of the dielectric thickness will eventually lead to plasma extinction or arcing respectively. This important issue has prevented detailed studies of DBDs in extreme environment, namely in high-speed airflows. In the present work, a solution to this technological problem has been found and is presented. Low temperature co-fireable ceramic (LTCC) technology allows, for the first time, to fully encapsulate the electrodes in a ceramic matrix and maximize the lifetime of the DBD system. Encapsulation improves the reproducibility of the experiments. Moreover, the plate can be manufactured in a curved shape. This technological advance permits, in the frame of the research presented here, to carry out a detailed experimental investigation of DBDs in high-speed flows. The goal of this experimental research is to improve the physical understanding of the interaction between a local atmospheric discharge, causing a localized weak ionization of the surrounding airflow, and the shock wave structure in transonic and supersonic flows typical for aeronautic applications. The fundamental nature of the research makes it relevant in a large domain of applications such as sonic boom alleviation, the reduction of aerodynamic losses (drag reduction) or combustion improvement. The surface dielectric barrier discharge is first characterized without airflow in order to understand the influence of the applied electrical conditions and the structure of the DBD plate on the discharge regime its spatial distribution. Current curves and photomultiplier measurements show that the DBD comprises a filamentary and a continuous (glow- or corona-like) component. Increasing the applied voltage ramp (dU2/dt) results in an increase in the filament generation rate and current peak amplitude. The geometry of the electrodes has little effect on the burning voltage but plays a role in the filament generation rate. Encapsulation reduces the rate of filament production and the expansion of the plasma around the upper electrode but it generates a more uniform distribution of the plasma on the surface and as a function of time. The behavior of the surface DBD in a high-speed air flow is first studied in a simple aerodynamic configuration: a flat DBD plate mounted on one wall of the nozzle. It is demonstrated that the DBD generated by this system can be sustained in supersonic airflows up to free stream Mach numbers of M∞=1.1. Current and time-resolved light emission measurements (photomultiplier) show that there are modifications in the discharge regime at high airflow velocity. For overall discharge, the filamentary to continuous component ratio is increased with increasing flow velocities, the plasma becomes relatively more filamentary. For individual microdischarges, the light pulse emission duration is reduced by one order of magnitude. These measurements indicate that there is a change in the breakdown mechanism and it is proposed that a transition from Townsend breakdown to streamer breakdown occurs when the airflow velocity is increased. The inverse problem is then addressed, the effects of the DBD on the airflow, in a case where the plasma is generated on the surface of an airfoil and interacts with the shock structure in the transonic flow field around that airfoil. Although no significant effects of the surface DBD on the normal shock generated in the transonic flow have been observed with the Schlieren visualizations and far-field pressure measurements, the flow modifies the plasma characteristics in a very significant way. In addition to the effects of the flow velocity (as observed in the flat plate experiment), the significant variation of pressure on the surface of the airfoil plays an important role. Decreasing pressure increases the number of filaments and favors high current peak generation. It shows that the discharge characteristics cannot be completely controlled and that they depend on the flow field.