Interest in the effects of magnetic field ergodization has recently increased within the magnetic confinement fusion community. Particularly in the physics of the plasma edge, the role of ergodic magnetic fields for transport and stability is being increasingly recognized. This interest is not only triggered by the hope to develop new methods for particle- and heat-exhaust in fusion reactors but also to gain a better understanding of transport around the stochastic tips of magnetic islands due to tearing mode instabilities. This special issue of Nuclear Fusion is intended to raise interest in the subject. The contents are based on presentations to the first Workshop on Stochastization in Fusion Edge Plasmas (SEP) held in Juelich, Germany, from October 6 to 8, 2003.Stimulated by the newly installed Dynamic Ergodic Divertor (DED) in the TEXTOR tokamak, this meeting was initiated by the various groups interested in the subject. The many participants came from different lines of fusion research, such as tokamak, stellarator and reversed field pinches. It is planned to continue the workshop biannually. The scope of the workshop will be broadened, including the transport properties of the inner plasma regions. The next workshop is planned for March 2005 again in Juelich. For details see http://www.fz-juelich.de/sep/.The main topics, represented by the various contributions to this special issue, are the identification of the structures of magnetic field lines in a partially open chaotic system; the modification of the energy and particle transport by stochastic fields; the interaction and amplification of error fields in magnetized plasmas; the penetration of rotating perturbation fields into such plasmas; the structure of such rotating fields and the resulting torque transfer; the reduction or elimination of ELMs in high confinement plasmas and the heat flux pattern due to ergodization and questions related to a helical or ergodic divertor, such as recycling and impurity screening. Ergodic magnetic field structures have to be inherently treated as a 3-d problem and the development of 3-d transport models is a key issue.We hope that this special issue of Nuclear Fusion will stimulate more interest in this fascinating subject of plasma physics.