The understanding of self-organized patterns in spatially extended nonlinear dissipative systems is one of the most challenging subjects in modern natural sciences. Such patterns are also referred to as dissipative structures. We review this phenomenon in planar low temperature dc gas-discharge devices with a high ohmic barrier. It is demonstrated that for these systems a deep qualitative understanding of dissipative structures can be obtained from the point of view of synergetics. At the same time, a major contribution can be made to the general understanding of dissipative structures. The discharge spaces of the experimentally investigated systems, to good approximation, have translational and rotational symmetry by contraction. Nevertheless, a given system may exhibit stable current density distributions and related patterns that break these symmetries. Among the experimentally observed fundamental patterns one finds homogeneous isotropic states, fronts, periodic patterns, labyrinth structures, rotating spirals, target patterns and localized filaments. In addition, structures are observed that have the former as elementary building blocks. Finally, defect structures as well as irregular patterns are common phenomena. Such structures have been detected in numerous other driven nonlinear dissipative systems, as there are ac gas-discharge devices, semiconductors, chemical solutions, electrical networks and biological systems. Therefore, from the experimental observations it is concluded that the patterns in planar low temperature dc gas-discharge devices exhibit universal behavior. From the theoretical point of view, dissipative structures of the aforementioned kind are also referred to as attractors. The possible sets of attractors are an important characteristic of the system. The number and/or qualitative nature of attractors may change when changing parameters. The related bifurcation behavior is a central issue of the synergetic approach chosen in the present article. A short review of possible theoretical approaches reveals that a theoretical description of the experimentally observed patterns is far from being satisfactory. Bearing this in mind, a qualitative model of the reaction-diffusion type is considered. Surprisingly enough, this model allows for a qualitative description of almost all fundamental patterns that have been observed experimentally. Also, so far the predictive power of this model is unmatched.