By stacking many very thin extraordinarily smooth sheets of material with a gap between each to form open channels, a new class of optical components for x-rays, ultraviolet light and neutrons can be made. Radiation propagates via grazing incidence reflections from the channel walls. If the stack is bent, radiation can be made to bend through large angles, and by properly forming the entrance or exit aperture, concentrators or collimators can be fabricated. This paper contains a discussion of the theory and fabrication of these laminar microchannel optics. Direct control over the reflecting surface and the stacking of the channels give these optics some unique advantages over other microchannel optics. Channel walls can be made as thin as 12 micrometers and coated with nearly any desired reflecting material and surface roughness below 2 angstroms can be readily achieved. Open spaces between the planar channels are as small as 8 micrometers or as large as desired. These optics provide the capability to bend, focus, or collimate broad energy bandwidths of radiation with optics that have apertures of up to several cm2, high throughput, and small size.