Many commercialized medicinal compounds are analogs of chemicals isolated from sources found in nature (also called natural products). However, the natural sources of these chemicals, such as plants, fungi, or insects, only offer small quantities of these bioactive agents. hus, it is typically desirable to find ways to synthesize these products and their analogs in large quantities using cost-effective methods that also minimize the impact on the environment. It is also important to develop strategies that expedite the process of modifying the natural products, which allows medicinal chemists to determine which functional groups are enhancing or deleterious to the bioactivity. In the Brewer lab, I have investigated organic reactions and methodologies with this aim -- to find ways to efficiently break and form carbon-carbon bonds, and to utilize these reactions in the total synthesis of structurally related natural products. The total synthesis of natural products is often used to showcase a methodology's utility by applying it in a more complex structure. The Lewis acid-promoted fragmentation of γ-silyloxy-β-hydroxy-α-diazo esters to provide tethered aldehyde ynoates was discovered and developed in the Brewer lab. This methodology was extended to bicyclic systems, in which the ring-fusion bond fragmented as a way to afford 10-membered ring ynones and ynolides, which are traditionally challenging to synthesize. This work will exhibit how the fragmentation reaction that provided 10-membered ynolides has the potential to lend itself to the synthesis of several structurally related, bioactive natural products via a divergent total synthesis strategy. In addition, this dissertation will describe our discovery that modifying the diazo carbonyl precursor to a β-hydroxy-α-diazo ketone changes the course of the Lewis acid-promoted reaction. Rather than a fragmentation sequence, the compound is converted to a vinyl cation, which undergoes a rearrangement then a C-H insertion of a second vinyl cation intermediate. This transition metal-free rearrangement/C-H insertion reaction provided cyclopentenone products. The migratory aptitudes of non-equivalent substituents in the cationic rearrangement step will also be discussed. Finally, the disparate reactivities of vinyl cations derived from diazo ketone, diazo ester, and diazo amide precursors will be detailed from an experimental and computational perspective. The results underscore the fact that this rearrangement and C-H insertion reaction may eventually be an effective way to prepare complex cyclopentyl-containing structures, which are common motifs in biologically active natural products.