We report the principal components of the C-13 chemical shift tensors for seven acylium ions, determined by both slow speed magic angle spinning (MAS) nuclear magnetic resonance (NMR) and theoretical methods. Experimentally, the acylium ions were prepared either by direct reaction of the parent acyl halides with metal halide powders, including frozen antimony pentafluoride, or by the reaction of alkyl halides with carbon monoxide on aluminum chloride (AlCl3). The generalization of our recent observation of the acetylium ion on AlCl3 to other cations is direct proof of free acylium ion intermediates in Friedel-Crafts acylation reactions. C-13 CP MAS NMR spectra of the acylium ions were acquired at temperatures ranging from 83 to 298 K, and the principal components of the C-13 chemical shift tensors were extracted by fitting the side band intensities of the MAS spectra. With the exception of the chloroacetylium ion, the acylium ions studied have isotropic C-13(1) chemical shifts of 154 +/- 1 ppm, but clear variations in the principal components of the shift tensors were measured. The carbenium carbons of the acetylium and 2,2-dimethylpropionylium ions have axially symmetric C-13 chemical shift tensors, consistent with the molecular symmetry (C-3 upsilon), while the chemical shift tensors of the other cations were characterized by non-zero asymmetry parameters. The observation of appreciably smaller chemical shift anisotropies for C-1 in the benzoylium ions versus the values for the corresponding carbon in the alkanoyl cations is consistent with charge delocalization into the ring substituent. Additional information on the acylium cations is provided by theoretical calculations. We optimized the geometries of the acylium ions using second-order Moller-Plesset perturbation theory (MP2) and the 6-311G* basis set. We then calculated the NMR data at the MP2 level using the gauge-including atomic orbital (GIAO) method and the double-zeta (dz) and triple-zeta polarized (tzp) basis sets of Horn and Ahlrichs. While the isotropic shifts calculated at the GIAO-RHF/tzp/dz level were in error by as much as 26 ppm, the GIAO-MP2 values were in excellent agreement with the experimental measurements, as were those for most of the principal components. The calculations were also used to determine the orientations of the principal components. The results of analysis of the MP2 wave functions help answer long standing questions regarding the structure and bonding of acylium cations.