Lens-based microscopy (such as light, phase contrast, fluorescence, confocal, and electron microscopy) has played an indispensable role in the evolution of modern sciences and technologies. Because x rays have much shorter wavelengths than visible light and a longer penetration depth than electrons, scientists have long dreamed of atomic resolution x-ray microscopes that could visualize the arrangement and dynamics of atoms in three dimensions. X-rays, however, are much more difficult to focus than electrons. By using x-ray optics, the smallest focal spot currently attainable is 30 nm for hard x rays and 15 nm for soft x rays. Furthermore, when the focal spot of soft x rays reaches 15 nm, the depth of focus becomes less than 0.5 um, which limits the thickness of the sample under investigation. In combination of coherent x-ray scattering with a method of direct phase recovery called oversampling, a novel form of lensless microscopy (i.e., x-ray diffraction microscopy), has recently been developed for imaging nanocrystals and noncrystalline specimens. The extension from two to three dimensions has also been pursued, which is based upon direct phase retrieval of a 3D diffraction pattern interpolated from a limited number of 2D patterns. However, since the diffraction intensity varies at least 5–7 orders from high to low resolution, reciprocal-space interpolation introduces artifacts in the assembled 3D diffraction pattern. The problem becomes even more severe for characterizing structure at the nanometer resolution,as more high-resolution data points need to be interpolated. Here, we report a new scheme for 3D x-ray diffraction microscopy through a combination of (i) ab-initio phase retrieval of 2D coherent diffraction patterns with a guided hybrid input-output algorithm and (ii) 3D image reconstruction with equally sloped tomography. The novelty of our x-ray microscope method is contained in the precision and reliability of both image reconstruction algorithms, and these innovations have allowed us to perform nondestructive and quantitative 3D characterization of materials at the nanometer scale resolution.