The electronic and magnetic properties of the luminescent excited states of colloidal Cu+:CdSe, Cu+:InP, and CuInS2 nanocrystals were investigated using variable-temperature photoluminescence (PL) and magnetic circularly polarized luminescence (MCPL) spectroscopies. The nanocrystal electronic structures were also investigated by absorption and magnetic circular dichroism (MCD) spectroscopies. By every spectroscopic measure, the luminescent excited states of all three materials are essentially indistinguishable. All three materials show very similar broad PL line widths and large Stokes shifts. All three materials also show similar temperature dependence of their PL lifetimes and MCPL polarization ratios. Analysis shows that this temperature dependence reflects Boltzmann population distributions between luminescent singlet and triplet excited states with average singlet-triplet splittings of similar to 1 meV in each material. These similarities lead to the conclusion that the PL mechanism in CuInS2, NCs is fundamentally different from that of bulk CuInS2 and instead is the same as that in Cu+-doped NCs, which are known to luminesce via charge-transfer recombination of conduction-band electrons with copper-localized holes. The luminescence of CuInS2 nanocrystals is explained well by invoking exciton self-trapping, in which delocalized photogenerated holes contract in response to strong vibronic coupling at lattice copper sites to form a luminescent excited state that is essentially identical to that of the Cu+-doped semiconductor nanocrystals.