AbstractA description is given of the models and resulting characteristics of the plasma adjacent to material surfaces that comprise the divertor and first wall of magnetic fusion energy devices under normal operation conditions. This thin edge-plasma region begins a short distance inside of the so-called separatrix, which divides the core domain of confined magnetic field lines from the scrape-off layer domain of open fields lines that pass through material surfaces; edge transport simulations give a unified description of the plasma throughout this region. In addition to the plasma fuel components escaping from the core (i.e. deuterium and tritium ions and their neutralizing electrons), models are included for neutral gas and impurities evolved from surfaces or injected. The confining magnetic field, B, is generally large enough to provide substantial enhancement of confinement normal to B compared to along B, resulting in steep cross-field gradients of plasma parameters. Three distinct types of edge-plasmas are illustrated, depending on the plasma collisionality, which are named as follows: sheath-limited, high-recycling, and detached plasmas. Examples of each type are given, together with the corresponding plasma conditions produced at the material surface boundaries. Detailed results are presented for the edge-plasmas of the ARIES-AT and FIRE tokamak designs. The edge-plasma characteristics calculated here provide the plasma profiles needed for other codes which perform detailed modeling of plasma sheath formation, surface modification via sputtering/redeposition, and recycled neutral-particle transport as detailed by other papers in this issue.