This collective book provides a review and summary of recent ten-year research in runaway electron preionized diffuse discharges (REP DD) formed in an inhomogeneous electric field in different gases at increased pressure. Attention is also given to volume (diffuse) discharges in a homogeneous electric field, barrier discharges, and so-called open low-pressure discharges. The book has contributions by research groups from different countries and institutes, which added much to the scope of data presented. New experimental techniques and equipment, including those with picosecond time resolutions, were required for diagnostics of electrical and optical signals. The book consists of 20 chapters, some of which were written jointly by researchers of different teams. We hope that this book will provide the reader with the unique opportunity to gain an insight into various aspects of runaway electron preionized diffuse discharges.