Although the sub-angstrom resolution of the modern transmission electron microscope (TEM) has made major contributions to defect structure analysis in many fields (such as oxides, interfaces, nanoparticles and superconductors) it has yielded little direct information on the core structure of dislocations. We suggest that “forbidden reflection” lattice images recorded in an ultra-high vacuum TEM in projections normal to the dislocation line could provide interpretable images of cores at atomic resolution. These could answer crucial questions, such as the nature of kinks, core reconstruction and periodicity, the nature of obstacles, and help distinguish obstacle theories of kink motion from the secondary Peierls-valley Hirth-Lothe theory. We give experimental forbidden reflection images and a new image obtained from silicon under UHV conditions with atomically smooth surfaces, whose preparation did not anneal out all dislocations. We also show experimental coherent nanodiffraction patterns and scanning transmission electron microscope (STEM) images recorded with the beam parallel to the core, so that core reconstruction can be expected to introduce a “half-order” Laue zone ring. We discuss the contribution that energy-loss spectroscopy from dislocation cores can be expected to make if a nanoprobe beam is used.