We have developed and fielded x-ray penumbral imaging on the National Ignition Facility in order to enable sub-10 μm resolution imaging of stagnated plasma cores (hot spots) of spherically shock compressed spheres and shell implosion targets. By utilizing circular tungsten and tantalum apertures with diameters ranging from 20 μm to 2 mm, in combination with image plate and gated x-ray detectors as well as imaging magnifications ranging from 4 to 64, we have demonstrated high-resolution imaging of hot spot plasmas at x-ray energies above 5 keV. Here we give an overview of the experimental design criteria involved and demonstrate the most relevant influences on the reconstruction of x-ray penumbral images, as well as mitigation strategies of image degrading effects like over-exposed pixels, artifacts, and photon limited source emission. We describe experimental results showing the advantages of x-ray penumbral imaging over conventional Fraunhofer and photon limited pinhole imaging and showcase how internal hot spot microstructures can be resolved.