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The ability to exhaust the plasma power loss from a large tokamak onto material walls surrounding the plasma has been perceived to be a large obstacle to the successful production of a fusion power reactor in the past. There have been tremendous strides in understanding the physics relevant to this power exhaust over the past five years. This improvement in understanding has arisen because of both improved diagnostics of the plasma outside the last closed flux surface, and because of improved two dimensional computer models of this plasma. This understanding has led to innovative plasma solutions that reduce the power load to the divertor region of ITER to levels that are acceptable for a successful engineering design of the divertors. These plasma solutions have been realized in the devices that are active today. 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 theoretical understanding of the plasma, neutral and atomic physics relevant to the plasma at the edge of fusion devices. Since understanding of the subject of this paper is progressing rapidly, we should emphasize that this paper was written in the spring of 1998 and, as such, presents the status of the subject at that time.