Calculations of Se-77 nuclear magnetic resonance chemical shifts and shieldings are reported for a number of selenium containing compounds. The calculated shifts span a range of about 2800 ppm, and therefore cover almost the complete range of known Se-77 chemical shifts. The calculations are based on density functional theory (DFT); gauge including atomic orbitals (GIAO’s) are used. The DFT-GIAO method is tested against other theoretical approaches. It is able to predict chemical shifts as well as individual tensor components of the shielding tensor with about the same quality as sophisticated ab initio methods. DFT is even capable of handling highly correlated systems like Se-4(2+). Other methods fail in this particular case.