The experimental and theoretical data on the X1Σg+, B1Σu+, and C1Πu states of H2, HD, and D2 are reviewed and an attempt is made to assess their respective reliabilities. Even where the data can be considered reliable, three kinds of discrepancy occur: (i) the total theoretical binding energy of the v = 0 state of X1Σg+ is too great, in contradiction to the variation theorem; (ii) the theoretical vibrational spacings are always too large; (iii) the theoretical rotational spacings for X1Σg+ are in good agreement with experiment, but for higher states there is a systematic disagreement between theory and experiment. It is concluded that (i) could be accounted for either by an error in the relativistic part of the theory or in the experiment; (ii) can only be accounted for by an error in the theory, probably in the nonrelativistic part; and (iii) simply results from the neglect of nonadiabatic coupling in the upper excited electronic states. In conclusion, new experiments and new calculations are recommended with a view to resolving these discrepancies.