The ability to exhaust the plasma power loss from a large tokamak ontomaterial walls surrounding the plasma has been perceived to be a large obstacle to thesuccessful production of a fusion power reactor in the past. There have beentremendous strides in understanding the physics relevant to this power exhaust overthe past five years. This improvement in understanding has arisen because of bothimproved diagnostics of the plasma outside the last closed flux surface, and becauseof improved two dimensional computer models of this plasma. This understanding has ledto innovative plasma solutions that reduce the power load to the divertor region ofITER to levels that are acceptable for a successful engineering design of thedivertors. These plasma solutions have been realized in the devices that are activetoday. Analysis using the improved plasma models also indicates that particle control,both of fuel and impurity particles, is adequate for successful operation of ITER.This paper presents the current status of both the experimental and theoreticalunderstanding of the plasma, neutral and atomic physics relevant to the plasma at theedge of fusion devices. Since understanding of the subject of this paper isprogressing rapidly, we should emphasize that this paper was written in the spring of1998 and, as such, presents the status of the subject at that time.