We present a study of optical properties of anatase (TiO2) using temperature and polarization dependent photoluminescence, optical absorption, and reflectance measurements. Anatase crystals, rutile crystals and thin TiO2 films have been studied in parallel for comparison purposes. Visible luminescence, due to the emission of self-trapped excitons, is observed in anatase. The optical absorption edge of anatase is 0.2 eV larger than that of rutile, and shows a dichroism of about 40 meV with respect to E parallel-to c and E perpendicular-to c polarizations at 10 K. The absorption edge of anatase displays an exponential energy dependence and is significantly less steep than the absorption edge of rutile. This may reflect the exciton self-trapping and/or the stronger influence of imperfections in anatase. For both anatase and rutile, the strongest interband transitions, governing the long-wavelength dispersion of the refractive index, appear as strong reflectivity maxima around 4 eV.