Methane and dinitrogen are abundant precursors to numerous valuable chemicals such as methanol and ammonia, respectively. However, given the robustness of these substrates, catalytically circumventing the high temperatures and pressures required for such transformations has been a challenging task for chemists. In this work, computational studies of various transition metal catalysts for methane C-H activation and N2 activation have been carried out. For methane C-H activation, catalysts of the form LnM=E are studied, where Ln is the supporting ligand (dihydrophosphinoethane or β-diketiminate), E the activating ligand (O, NCH3, NCF3) at which C-H activation takes place, and M the late transition metal (Fe,Co,Ni,Cu). A hydrogen atom abstraction (HAA) / radical rebound (RR) mechanism is assumed for methane functionalization (CH4 à CH3EH). Since the best energetics are found for (β-diket)Ni=O and (β-diket)Cu=O catalysts, with or without CF3 substituents around the supporting ligand periphery, complete methane-to-methanol cycles were studied for such systems, for which N2O was used as oxygen atom transfer (OAT) reagent. Both monometallic and bimetallic OAT pathways are addressed. Monometallic Fe-N2 complexes of various supporting ligands (LnFe-N2) are studied at the beginning of the N2 activation chapter, where the effect of ligand on N2 activation in end-on vs. side-on N2 isomers is discussed. For (β-diket)Fe-N2 complexes, the additional influence of diketiminate donor atom (N(H) vs. S) is briefly addressed. The remainder of the chapter expands upon the treatment of β-diketiminate complexes. First, the activation and relative stabilities of side-bound and end-bound N2 isomers in monometallic ((β-diket)M-N2) and bimetallic ((β-diket)M-N2-M(β-diket)) first row transition metal complexes are addressed. Second, the thermodynamics of H/H+/H- addition to (β-diket)Fe-bound N2, followed by subsequent H additions up to release of ammonia, is discussed, for which two mechanisms (distal and alternating) are considered. Finally, the chapter concludes with partial distal and alternating mechanisms for H addition to N2 in bimetallic (β-diket)Fe-N2-Fe(β-diket) and (β-diket)M-N2-M(β-diket) (M = Ti,V,Fe), respectively.