In this letter, we discuss the electronic structure of copper aluminate (CuAlO2) on the basis of absorption measurements at low temperature and under high pressure in single crystals and thin films, combined with ab initio electronic structure calculations. The indirect character of the fundamental transition could be clearly established through the photon energy dependence of the absorption edge as measured in single crystals, yielding a band gap (plus a phonon) of 2.99±0.01 eV at room temperature. An indirect excitonic structure is also observed at low temperature. The lowest energy direct allowed transition occurs near 3.53±0.01 eV and is identified through its low-energy tail in single crystals and its excitonic peak in thin films. Comparing our results with ab initio calculations available in the literature, we conclude that CuGaO2 and CuInO2 can hardly be considered as wide gap semiconductors, even if they are transparent in thin films.