Those who study new reactions and their selectivities are often driven by an interest in developing novel, practical methods that can be exploited to achieve complex chemical transformations over a small number of synthetic steps. The ultimate goal of such efforts is to achieve step economy, an overarching principle of green chemistry that minimizes reagents, waste, and production time. The design and application of metal-catalyzed and light-mediated cycloadditions is one important avenue of research, as such transformations can be atom economical and, more importantly, can create multiple bonds, rings, and stereocenters in a single step toward targets of high complexity and value. Linked to the development of new reactions is the design and understanding of new catalysts and ligands possessing novel reactivities and selectivities. Step economy can also be achieved by the clever streamlining of multiple transformations into a single synthetic operation, thus further reducing material and personnel costs. Such single-flask serial/cascade reactions can be used for the rapid assembly of molecular scaffolds, some of which comprise the core of targets with exciting physical properties or biological activity. The research presented in this dissertation addresses all of these themes. Within the context of similar reactions of activated, strained rings, Chapter 1 introduces the metal-catalyzed [5+2] cycloaddition of vinylcyclopropanes (VCPs) and pi-systems for the construction of seven-membered rings, an important motif in many natural products and natural-product-inspired synthetic targets. Chapter 2 describes the latest advancements in new catalysts and new ligands for the strategically convergent and operationally simple rhodium(I)-catalyzed intermolecular [5+2] reactions of VCPs and alkyne feedstocks. In Chapter 3, the regioselectivity of intermolecular [5+2] cycloadditions is explored systematically, as unsymmetrical substrates can give rise to multiple regioisomeric cycloadducts depending upon the orientation of the alkyne during a postulated (turnover-limiting) migratory insertion mechanistic step. Chapters 4 and 5 illustrate the development and application of single-flask / serial reactions involving the [5+2] cycloaddition, making use of the catalysts and insights from Chapters 2 and 3. In Chapter 4, an intermolecular [5+2] cycloaddition of enynones and VCPs, followed by a Nazarov cyclization, is envisioned for strategically novel and rapid access to the bicyclo[5.3.0]decane skeleton from readily available components. Chapter 5 describes the evolution of a project that, guided by the principles of function-oriented synthesis to access the minimally necessary chemical space for function via the fewest synthetic steps, uses serial [5+2]/[4+2] cycloadditions to assemble novel, potent inhibitors of protein kinase C (PKC). Lastly, Chapter 6 describes a total synthesis of penifulvin A, a sesquiterpenoid metabolite reported as the first example of a naturally occurring dioxa[5,5,5,6]fenestrane. The synthetic strategy features the use of an arene-alkene meta photocycloaddition as the key complexity-generating reaction.