Laser-cooled ions in a trap can be strongly coupled and form crystalline states. We describe experimental studies that measure the spatial correlations of the ion crystals formed in Penning traps. Both Bragg scattering of the cooling-laser light and spatial imaging of the laser-induced ion fluorescence are used to measure these correlations. In spherical plasmas with more than2×105ions, body-centered-cubic (bcc) crystals, the predicted bulk structure, are the only type of crystals observed. We are able to phase-lock the orientation of the ion crystals to a rotating electric-field perturbation. With this “rotating wall” technique and stroboscopic detection, images of individual ions in a Penning trap are obtained. The rotating-wall technique also provides a precise control of the time-dilation shift due to the plasma rotation, which is important for Penning trap frequency standards. ©1999 American Institute of Physics.