An equilibrium bond length of r(e) = 1.894 Angstrom and harmonic vibrational frequency of omega(e) = 664 cm(-1) are computed for IO(X-2 Pi) at the nonrelativistic all-electron CCSD(T)/6-311+G(3df) level of theory. These are within 1% of the experimental Omega-averaged values of 1.877 +/- 0.005 Angstrom (3 sigma) and 670 +/- 13 cm(-1) (3 sigma), respectively. Similar calculations predict r(e)=1.824 Angstrom and omega(e)=764 cm(-1) for IO+ (X-3 Sigma(-)). For the singlet excited electronic states of IO+, which require a multireference treatment, CASPT2(8,6)/6-311+G(3df) predicts r(e)=1.841 Angstrom and omega(e)=738 cm(-1) for IO+(a(1) Delta) and r(e)=1.870 Angstrom and omega(e)=679 cm(-1) for IO+(b(1) Sigma(+)). The equilibrium bond length increases and the harmonic vibrational frequency decreases from the ground to the excited states of IO+ as observed for the isovalent O-2 molecule. A spin-spin splitting of 1060 +/- 160 cm(-1) (3 sigma) is assigned to the two sublevels of the ground state of iodine monoxide cation, IO+ (X-1(3) Sigma(0)(-), X-2(3) Sigma(+/-1)(-)), on the basis of a reinterpretation of an experimental photoionization efficiency spectrum of IO. This reassignment is required by the present vibrational constants for IO+, Franck-Condon factors, and four-component, relativistic multireference configuration interaction (CI) calculations of the spin-spin splitting. An adiabatic ionization energy of 9.60 eV is computed at the CCSD(T) level of theory for the IO+(X-3 Sigma(0)(-)) <-- IO(X-2 Pi(3/2)) transition and is in reasonable agreement with the experimental photo-ionization threshold of 9.735 +/- 0.017 eV (3 sigma). Adiabatic excitation energies of 0.72 and 1.18 eV are calculated at the CASPT2 level of theory for IO+(a(1) Delta) <-- IO+(X-3 Sigma(0)(-)) and IO+(b(1) Sigma(+)) <-- IO+(X-3 Sigma(0)(-)) transitions, respectively. The photoionization spectrum of IO and excitation spectrum of IO+ have also been simulated.