The combination of a nonthermal plasma and a heterogeneous catalyst provides unique opportunities for chemical transformations. High densities of reactive species, such as ions, radicals or vibrationally excited molecules, are generated by electron collisions and initiate a multitude of chemical reactions in the gas phase. By shifting the reaction site from the gas phase to the surface of the catalyst, the selectivity of these reactions can be significantly enhanced. Dielectric barrier discharges (DBDs) are a promising plasma source for these kinds of applications due to their non-equilibrium conditions and their simple construction. This review provides a brief introduction to the breakdown mechanism and the various geometries of DBDs and presents several plasma-catalytic DBD applications.