Deep x-ray lithography, together with high quality electrogrowth (LIGA) is known for its capacity in fabricating extreme high aspect ratio structures of very good sidewall roughness and perpendicularity. Since LIGA-resists are plastics, and elastically deformable, we describe the physics and fabrication of Orthogonal Reflection Optics (ORO), LIGA- based multimirror lenses. Such optics operate by reflections from precisely inclined sidewalls. Diffraction calculations show excellent behavior in comparison even to Fresnel zone plates. OROs produce piecewise linear approximations of ideal lenses and can perform accordingly. Unlike classical lenses, OROs may work well in the VUV and soft x-ray region, and even for hard x-rays or function as particle-optics. OROs can be designed intrinsically achromatic. OROs are lightweight, quite planar and a large number of material choice exists for adjusting lens behavior to desired functions, e.g. high melting point metals (Pt, Os) for very heat resistant lenses operating above 2000 K. A classification of an entire ORO family, together with other modern concepts concerning x-ray micro transmission lenses by micromachining is included. First fabrications of 2D and 1D planar ORO-Fresnel lenses by LIGA are described.