We summarize the experimental observation of a large variety of self‐organized patterns in the electrical current density of the discharge space of planar gas‐discharge systems with high impedance electrodes. In the center of interest are static and dynamic well‐localized solitary patterns (dissipative solitons, DSs) and their interaction leading e.g. to scattering, the formation of “molecules”, generation, annihilation and the formation of patterns of higher complexity consisting of DSs. A simple 3‐component reaction‐diffusion system qualitatively takes account of most of the observed phenomena. In addition, we present a rigorous reduction of these equations to a set of ordinary differential equations near the transition point from a stationary to a travelling DS, giving a mathematical foundation of a description of DSs as particles. © 2004 American Institute of Physics