The electronic structures of CuX2 (X=Cl and Br) have been investigated in the gas phase by means of anion photodetachment photoelectron spectroscopy and ab initio theory. The photoelectron spectra of CuX2- were recorded at two photon energies, 193 and 157 nm. Well-resolved and rich photodetachment features in the spectra provide unprecedented details for the low-lying electronic states of CuCl2 and CuBr2. The excitation energies for five low-lying electronic states of CuX2 were determined, and they explain well the two previously observed optical absorption bands. The electron affinities for CuCl2 and CuBr2 were determined to be identical, 4.35 +/-0.05 eV within the experimental uncertainty. Both the anions and neutral CuX2 species were calculated to be linear with only a slight bond length variation between the charged and neutral species. The calculated electron affinities and vertical excitation energies for the excited states agree well with the experimental values, yielding a definite assignment for the electronic states of CuCl2 and CuBr2.