[en] Ionization cross sections for heavy ions and electrons incident on various atoms and molecules are required in the modeling of the interaction of radiation with matter. For each case, the energy distribution of secondary electrons (the single differential cross section, SDCS) is needed over a broad range of projectile and secondary electron (delta-ray) energies. In many cases the energy and angular distribution of secondary electrons (the double differential cross section, DDCS) is also necessary. Clearly, it would be desirable to have laboratory SDCS and DDCS measurements for all of the cases required. For a variety of reasons, this is not yet possible. Thus, one must turn elsewhere to obtain the needed cross sections. In this paper, we discuss cross sections obtained in two different ways; ab initio theory based on the first Born approximation, and a semi-empirical method based on the Bethe-Born Approximation. In both cases, results on helium will be presented since the largest amount of data is available in this case. Applications of both methods to other target species are given in the references. The accuracy of the methods and plans for the near future are also discussed. 23 references, 6 figures