Hollow-anode glow discharge apparatus in the form of two-electrode and three-electrode reactors provide, in various embodiments, improved uniformity, efficiency and low-pressure substrate surface processing. In one improved uniformity embodiment for ion-dominated processes, the apparatus of the invention includes a high-energy-density uniformizing grid having multiple, multi-sized and evenly-spaced holes. In one improved uniformity embodiment for chemically-dominated processes, the apparatus of the invention includes a high-energy-density uniformizing grid having multiple, evenly-spaced holes and a stepped or continuously-variable non-planar profile. In one improved low pressure embodiment for ion-dominated and/or chemically-dominated processes, the apparatus of the invention includes a high-energy-density grid having multiple, evenly-sized and spaced holes of widths large enough to overcome dark space effects. In one improved efficiency selected ion energy embodiment for ion-dominated and/or chemically-dominated processes, the apparatus of the invention includes a high-energy-density source that synergistically cooperates with an apertured grid to provide selected-energy ions at higher densities than heretofore possible. In any embodiment, both build-up on and removal from the substrate are possible.