This paper is a state of the art of the understanding on the physics of homogeneous dielectric barrier discharges at atmospheric pressure. It is based on the analysis of present and previous work about the behavior of these discharges and the conditions to get them. Mechanisms controlling the homogeneity during gas breakdown and discharge development are successively discussed. The breakdown has to be a Townsend one, the ionization has to be slow enough to avoid a large avalanche development. During the breakdown, the discharge homogeneity is related to the ratio of the secondary emission at the cathode (γ coefficient) on the ionization in the gas bulk (α coefficient). Higher is this ratio, higher is the pressure × gas gap product (Pd) value for which a Townsend breakdown is obtained. Among the phenomena enhancing the secondary emission there is the negative charge of the dielectric on the cathode surface, the trapping of ions in the gas and the existence of excited state having a long lifetime compared to the time between two consecutive discharges. The first phenomenon is always present when the electrodes are covered by a solid dielectric, the second one is related to the formation of a positive column and the third one is specific of the gas. During the discharge development, the homogeneity is mainly controlled by the voltage or the current imposed by the electrical circuit/electrode configuration and by the gas ability to be slowly ionized. Larger is the contribution of a multiple step ionization process like Penning ionization, higher will be the working domain of the discharge. A decrease of the gas voltage during the discharge development is a solution to enhance the contribution of this process. After 20 years of research a lot of mechanisms have been understood however there is still open questions like the nature of the Inhibited homogeneous DBD, surface energy transfers, role of attachment and detachment...