Many modern industrial processes and research applications place increasingly higher demands on x-ray computed tomography (CT) imaging resolution and sensitivity for low-contrast specimens with a low atomic number. The three approaches to increasing imaging resolution are (1) reduction in the x-ray spot size, (2) use of higher resolution detectors or (3) employment of x-ray optical elements. Systems that pursue one or more of these approaches are available and under continued development. The Xradia MicroXCT™ projection-type microscope described in this paper has been optimized for high-resolution x-ray CT by employing a high-resolution detector paired with a microfocus x-ray source. Large working distances in this CT system enable full tomographic data collection at micrometre resolution of large samples, such as flip-chip packages. X-ray CT instruments using x-ray optical elements for condenser optics and imaging objective lenses are a new development capable of reaching sub-50 nm resolution. These instruments find various applications, including die-level imaging in the semiconductor industry as well as the process development for fuel cells, which we describe here as one application. Sub-micron resolution CT instruments without x-ray optical elements have a large application base already; however, new instruments optimized for soft materials and low-contrast specimens, such as the Xradia nanoXCT™, offer completely new capabilities and open new applications. New developments in the area of phase contrast imaging enable unprecedented image contrast for specimens with very low absorption, which for research applications enables for the first time the imaging of many specimens in their natural state (e.g., arteries to examine calcification). Zernike phase contrast for sub-50 nm x-ray CT even enables the imaging of single cell or thin tissue slices for biological or medical applications.