In this dissertation, my aim is to study different type of under-explored N-Heterocyclic Carbenes (NHC) complexes of Ir and Rh. These complexes have been synthesized, and the reaction mechanism, solution dynamics, and catalytic activity studies are presented in this dissertation. In Chapter 2 shows that phosphine-tethered imidazolium ions can undergo C-H oxidative addition when treated with [Ir(COD)Cl]2 to give abnormal iridium(III) NHC hydrides. The effects of the length of the linker, the kinetic studies of C-H activation and catalytic application of these complexes are systematically studied. Chapter 3 describes the synthesis of iridium and rhodium complexes stabilized by 2-methyleneimidazoline ligands via highly selective intramolecular activation of 2-methyl C-H vs C4/5-H bonds of the imidazolium moieties with the chelation assistance of phosphine ligands. The selectivity of C(sp3)-H vs C(sp2)-H activation, the conversion of methyleneimidazoline to abnormal complex and the electronic properties of ligands are also presented.