Dislocations and their interactions strongly influence many material properties, ranging from the strength of metals and alloys to the efficiency of light-emitting diodes and laser diodes(1-4). Several experimental methods can be used to visualize dislocations. Transmission electron microscopy (TEM) has long been used to image dislocations in materials(5-9), and high-resolution electron microscopy can reveal dislocation core structures in high detail(10), particularly in annular dark-field mode(11). A TEM image, however, represents a two-dimensional projection of a three-dimensional (3D) object (although stereo TEM provides limited information about 3D dislocations(4)). X-ray topography can image dislocations in three dimensions, but with reduced resolution(12). Using weak-beam dark-field TEM13 and scanning TEM14, electron tomography has been used to image 3D dislocations at a resolution of about five nanometres (refs 15, 16). Atom probe tomography can offer higher-resolution 3D characterization of dislocations, but requires needle-shaped samples and can detect only about 60 per cent of the atoms in a sample(17). Here we report 3D imaging of dislocations in materials at atomic resolution by electron tomography. By applying 3D Fourier filtering together with equal-slope tomographic reconstruction, we observe nearly all the atoms in a multiply twinned platinum nanoparticle. We observed atomic steps at 3D twin boundaries and imaged the 3D core structure of edge and screw dislocations at atomic resolution. These dislocations and the atomic steps at the twin boundaries, which appear to be stress-relief mechanisms, are not visible in conventional two-dimensional projections. The ability to image 3D disordered structures such as dislocations at atomic resolution is expected to find applications in materials science, nanoscience, solid-state physics and chemistry.