Barrier discharges, also known as dielectric-barrier discharges or silent discharges, provide a simple technology to establish nonequilibrium plasma conditions in atmospheric-pressure gases. This property has led to a number of industrial applications, including ozone generation, surface modification, pollution control, CO2 lasers, excimer lamps, and flat plasma-display panels. Depending on a variety of gas properties, operating parameters, and boundary conditions, the discharge can exhibit pronounced filamentary character, self-organized regular-discharge patterns, or completely diffuse appearance. The literature on these different types of barrier discharges is reviewed, and the underlying physical phenomena are discussed. Relative recent investigations on low-current density diffuse barrier discharges suggest novel applications of fairly "mild" plasmas for sterilization and disinfection purposes and utilizing their selective influence on biological cells.