Catalysis of metal carbene transformations with selected dirhodium(II) catalysts is a useful technology for constructing complex polycycles via intramolecular cyclopropanation, C-H insertion, and ylide derived reactions of diazoacetates and diazoacetoacetates. In this thesis, novel methodologies based upon intramolecular C-H insertion and the oxonium ylides rearrangements are investigated, and a new understanding of oxonium ylide formation and rearrangements is presented. In chapter 1, in work done under the supervision of Dr. Herman O. Sintim, a novel methodology for the synthesis of enantiopure tertiary alcohols is described. The key step in the methodology is an intramolecular C-H insertion reaction whereby a new connector between a carbene center and the C-H target, the N-O tether, is introduced. The resulting C-H insertion products were converted to tertiary-amino alcohols via cleavage of the N-O tether. This approach allows the regioselective insertion of metal carbenes into the C-H bond alpha to a heteroatom and leads to the formation of tertiary stereocenters. Key concepts are outlined that aim at achieving selectivity in C-H insertion using a new tether that facilitates the construction of five membered rings, thus enabling remote functionalization of complex molecules. In chapter 2, a detailed analysis of the mechanism of oxonium ylide generation and rearrangement, which has not been previously reported, was performed to gain insight into the mechanistic pathway by which oxonium ylides rearrange. The mechanism was studied via the synthesis of oxabicyclo[4.2.1]nonane compounds. Catalytic ylide formation and subsequent [1,2]-Stevens rearrangement unexpectedly resulted in a 70:30 molar ratio of two diastereoisomers formed in high yield. There was negligible dependence of the ratio of the two diastereoisomers on either para substituents on the aromatic ring or on the catalyst employed. However, the use of a large aryl substituent (e.g., anthranyl, mesityl, and 2,6-dimethyl-4-nitrophenyl) resulted in the formation of a single diastereoisomer. The importance of the size of the aryl group, coupled with the absence of a substituent effect on the ratio of the [1,2]-Stevens rearrangement diastereoisomers suggest that conformational influences are responsible for the apparent isomerization. Each diazoacetoacetate conformer forms a different oxonium ylide and subsequent rear rangement of each of these oxonium ylides leads to the formation of a distinct diastereoisomeric product. In chapter 3, the mechanism of oxonium ylides rearranging via the [2,3]- sigmatropic rearrangement pathway was also investigated. Rh(II) catalyzed oxonium ylide generation of trans-3-styryltetrahydropyranone-5-diazoacetoacetates and its subsequent rearrangement forms two diastereoisomers in both the [1,2]-Stevens and [2,3]-sigmatropic processes. The two diastereoisomers of the [2,3]-sigmatropic processes, (78:22) molar ratio, are formed in high yield, but with negligible dependence on either para substituents on the aromatic ring or on the catalyst employed. The formation of a second diastereoisomer for the symmetry-allowed concerted [2,3]-sigmatropic rearrangement process is supportive of a concerted mechanism leading to the two diastereoisomers of the [2,3]-sigmatropic processes via the presence of two conformational isomers of trans-3-styryltetrahydropyranone-5 diazoacetoacetates.