Barrier discharges (BDs) produce highly non-equilibrium plasmas in a controllable way at atmospheric pressure, and at moderate gas temperature. They provide the effective generation of atoms, radicals and excited species by energetic electrons. In the case of operation in noble gases (or noble gas/halogen gas mixtures), they are sources of an intensive UV and VUV excimer radiation. There are two different modes of BDs. Generally they are operated in the filamentary one. Under special conditions, a diffuse mode can be generated. Their physical properties are discussed, and the main electric parameters, necessary for the controlled BD operation, are listed. Recent results on spatially and temporally resolved spectroscopic investigations by cross-correlation technique are presented. BDs are applied for a long time in the wide field of plasma treatment and layer deposition. An overview on these applications is given. Selected representative examples are outlined in more detail. In particular, the surface treatment by filamentary and diffuse BDs, and the VUV catalyzed deposition of metallic layers are discussed. BDs have a great flexibility with respect to their geometrical shape, working gas mixture and operation parameters. Generally, the scaling-up to large dimensions is of no problem. The possibility to treat or coat surfaces at low gas temperature and pressures close to atmospheric once is an important advantage for their application.