We present ab initio calculations of the electronic structure and the optical properties of InN. They are based on a combination of the solutions of the Kohn-Sham equation and quasiparticle corrections. The results are critically discussed in the light of recent experiments. We find an energy gap of InN < 1 eV and a non-parabolic absorption edge. (C) 2002 Elsevier Science B.V. All rights reserved.