X-rays have been widely used in the structural analysis of materials because of their significant penetration ability, at least on the length scale of the granularity of most materials. This allows, in principle, for fully three-dimensional characterization of the bulk properties of a material. One of the main advantages of x-ray diffraction over electron microscopy is that destructive sample preparation to create thin sections is often avoidable. A major disadvantage of x-ray diffraction with respect to electron microscopy is its inability to produce real-space images of the materials under investigation—there are simply no suitable lenses available. There has been significant progress in x-ray microscopy associated with the development of lenses, usually based on zone plates, Kirkpatrick–Baez mirrors, or compound refractive lenses. These technologies are far behind the development of electron optics, particularly for the large magnification ratios needed to attain high resolution. In this article, the authors report progress toward the development of an alternative general approach to imaging, the direct inversion of diffraction patterns by computation methods. By avoiding the use of an objective lens altogether, the technique is free from aberrations that limit the resolution, and it can be highly efficient with respect to radiation damage of the samples. It can take full advantage of the three-dimensional capability that comes from the x-ray penetration. The inversion step employs computational methods based on oversampling to obtain a general solution of the diffraction phase problem.