Theoretical studies on ethylene polymerization by single site homogeneous catalysts, as well as by Ziegler-Natta heterogeneous catalysts, have been reviewed. Studies on cation-anion interactions in ion-pair systems of the typeprovided indications as to which ancillary ligands on the cation acted as good electron donors, and also revealed the importance of having a weakly coordinating anion to enable the ionpair to separate more easily in solution. Subsequent calculations of barriers to ethylene insertion into the metal-methyl bond in ionpair systems of the type LL 0 MeM-l-B(C 6 F 5 ) 3 [M ¼ Ti, Zr] revealed that the ease of separation of the anion from the cation in solution was an important criterion in determining the activity of the catalysts. The barrier to insertion was found to be the rate determining step during the first insertion of ethylene into the metal-methyl bond, but second insertion studies conducted for two different ion-pair systems showed that the barrier to uptake of the monomer became the rate determining step during the second insertion of the ethylene monomer. Theoretical studies conducted on TiCl 4 /MgCl 2 heterogeneous Ziegler-Natta catalysts provided insights into the nature of the binding of the titanium catalysts (with the Ti in different oxidation states) on to the MgCl 2 support.The results indicated that the support worked best when a few Ti atoms replaced Mg atoms in the crystal lattice of the support. Ethylene polymerization studies, along with investigations on chain termination, led to the conclusion that the TiCl 3 -based edge site on MgCl 2 would be the most promising model for the actual catalytic species. Studies on addition of tetrahydrofuran (THF) to the active sites showed that the presence of the base would lead to higher molecular weights of the polymers, as it acted to increase the barrier to termination (by chain transfer to monomer) more than the barrier to insertion.