The orientation dependence of aluminum chemical shielding is shown to vary from a few ppm in distorted octahedral complexes to more than 400 ppm in linear molecules. The analysis of solid-state Al-27 NMR spectra of tris(acetylacetonato)aluminum(III), Al(acac)(3), and tris(tropolonato)aluminum(III), Al(trop)(3), obtained at three different applied magnetic fields (4.7, 9.4, and 18.8 T) reveal small Al-27 chemical shielding anisotropies of 3.8(3) and 9.0(3) ppm, respectively. Similarly, analysis of solid-state Al-27 MMR spectra of tris(2,2,6,6-tetramethyl-3,5-heptanedionato) -aluminum(III), AI(TMHD)(3), at 4.7 and 9.4 T yield an Al-27 chemical shielding anisotropy of 6.7(5) ppm. Aluminum nuclear quadrupole coupling constants, asymmetry parameters, and the relative orientations of the chemical shielding (CS) and electric field gradient (EFG) tensors are also reported. The utility of obtaining and analyzing solid-state NMR spectra at high applied magnetic field strengths is demonstrated. Aluminum nuclear spin-rotation constants available from recent high-resolution Fourier transform microwave spectroscopy studies of aluminum(I) isocyanide (AlNC) and aluminum(I) chloride (AlCl) indicate large Al-27 CS anisotropies of 406(9) and 477(17) ppm, respectively. Experimental results are compared with theoretically-calculated CS and EFG parameters, using both restricted Hartree-Fock methods and density functional theory.