The existing theoretical cross section data for the charge exchange process of multiply charged fully stripped ions with hydrogen atoms are evaluated in the energy range from ∼10 eV/u to ∼103keV/u. The evaluation has been performed on the basis of both pure theoretical arguments and comparison with the most accurate experimental cross sections. The ionic charge state ranges fromZ=2 toZ=54. The theoretical methods for calculation of the charge exchange cross sections are briefly discussed, and their regions of validity and the accuracy of the produced data are assessed.