[en] This review attempts to provide an analysis of the theoretically produced data and of the theoretical models employed, for charge exchange between positive ions and atomic hydrogen. The overall objective is to provide a selection of the most reliable theoretical data and of the most reliable models for producing new data, keeping in mind the priorities that have been established in the current thermonuclear fusion research programs. The cross sections of interest are both the total cross section and the partial cross sections leading to electron capture into a given final state