Vertical excitation energies up to about 9 eV, and related oscillator strengths, were calculated by multireference configuration interaction (MRCI) methods for singlet and triplet states of BrOBr in C-2v symmetry, including the low-lying s- and p-Rydberg states. Observed maxima in the visible/UV spectra were identified as excitations to 1(3)B(1) (665 nm, 1.86 eV), 1(1)B(1) (520 nm, 2.38 eV), 1(1)B(2) (355 nm, 3.49 eV), 2(1)A(1) (314 nm, 3.94 eV), and 3(1)B2, (similar to 200 nm, similar to 6.20 eV). The calculated vertical excitation energies lie within 0.1 eV of the observed values. Many more singlet and weaker triplet excitations are predicted. Although most excited states have small oscillator strengths, that of 3(1)B(2) is very large. Vertical excitation energies were also calculated at the 1(1)A' ground state geometry of the BrBrO isomer. Using DFT/B3LYP and CCSD(T) (CC) methods with the 6-311+G(3df) basis set, geometries were optimized for about 12 excited singlet and triplet states of BrOBr in C-2v symmetry. Frequency analysis showed that many states, including 1(1)B(1), 1(1)B(2), 1(3)B(1), and 1(3)B(2), are not stable. Cs structures corresponding to 1(1)B(1), 1(3)B(1), and 1(3)B(2) were optimized. In addition, geometry optimizations were performed for the lowest singlet and triplet A' and A" states of BrBrO. This isomer lies 0.61 (CC) to 0.66 eV (MRCI) above BrOBr. Comparison was made with the lowest excited states of Cl2O and F2O.