In industries, the dielectric barrier discharge systems are operated at atmospheric pressure which show the advantages for surface processing and plasma chemistry. Typically, two electrodes separated by several millimeters and operated with sinusoidal A.C. voltage with frequency in range of tens kHz. The dielectric layer between two electrodes can greatly limit the strength of the discharge current. In filamentary discharge regime, small discharge channels are formed in the gaseous layer which look like bright filaments. Despite the filamentary discharge is widely applied to the industrial products, the discharge mechanism is not clear. In our research, the filamentary discharge is investigated with different electrode geometries. The gap dependence of the discharge is briefly discussed. The breakdown mechanism of single filamentary discharge is investigated in the needle-to-plane electrodes setup which shows consistent scaling relation with electron avalanche. The interaction between the filamentary discharges is investigated in the plane-toplane electrodes setup. The disorder-order transition of the discharge spots is observed as the increase of the gap distance. It is found that the structural transition of the filamentary discharges is strongly related to the mutual Coulomb interaction between the charge piles. Finally, we report the investigation of the filamentary discharges in the wedged plane-to-plane electrodes setup. As the gap distance increases, the continuous structural transition of the discharge pattern is found. We further confirm the discharge process is dominated by the gap distance.