This work discusses the C-H bond activation by transition metal complexes using various computational methods. First, we performed a DFT study of oxidative addition of methane to Ta(OC2H4)3A (where A may act as an ancillary ligand) to understand how A may affect the propensity of the complex to undergo oxidative addition. Among the A groups studied, they can be a Lewis acid (B or Al), a saturated, electron-precise moiety (CH or SiH), a σ-donor (N), or a σ-donor/π-acid (P). By varying A, we seek to understand how changing the electronic properties of A can affect the kinetics and thermodynamics of methane C–H activation by these complexes. For all A, the TS with H trans to A is favored kinetically over TS with CH3 trans to A. Upon moving from electron-deficient to electron-rich moieties (P and N), the computed C–H activation barrier for the kinetic product decreases significantly. Thus, changing A greatly influences the barrier for methane C–H oxidative addition by these complexes. Secondly, a computational study of oxidative addition (OA) of methane to M(OC2H4)3A (M = Ta, Re and A = ancillary ligand) was carried out using various computational methods. The purpose of this study was to understand how variation in A and M affects the kinetics and thermodynamics of OA. Results obtained from MP2 calculations revealed that for OA of CH4 to Re(OC2H4)3A, the order of ΔG‡ for a choice of ancillary ligand is B > Al > SiH > CH > N > P. Single point calculations for ΔG‡ obtained with CCSD(T) showed excellent agreement with those computed with MP2 methods. MCSCF calculations indicated that oxidative addition transition states are well described by a single electronic configuration, giving further confidence in the MP2 approach used for geometry optimization and ΔG‡ determination, and that the transition states are more electronically similar to the reactant than the product. Thirdly, a computational study of olefin polymerization has been performed on 51 zirconocene catalysts. The catalysts can be categorized into three classes according to the supporting ligand framework: Class I - Cp2ZrCl2 (ten catalysts), Class II - CpIndZrCl2 (thirty-eight catalysts), and Class III - Ind2ZrCl2 (three catalysts), Cp = η5-cyclopentaidenyl, Ind = η5-indenyl. Detailed reaction pathways, including chain propagation and chain termination steps, are modeled for ethylene polymerization using Class II catalysts. Optimized structures for reaction coordinates indicated the presence of α-agostic interactions in the transition states (TSs) for both the 1st and 2nd ethylene insertions as well as in the ethylene π-complex of the Zr-nPr cation. However, β-agostic interactions predominate in the cationic n-propyl and n-pentyl intermediates. The calculated relative Gibbs free energies show that the TS for insertion of ethylene into the Zr-CH3+ bond is the highest point on the computed reaction coordinates. This study, in concert with previous work, suggests that the type of ring attached to Zr (Cp vs. Ind) affects the reaction kinetics and thermodynamics less significantly than the type of substituents attached to the Cp and indenyl rings, and that substituent effects are even greater than those arising from changing the metal (Zr vs. Hf)