This dissertation summarizes a number of computational chemistry strategies used to study organic reactions, specifically pericyclic reactions and non-classical carbocations. Chapter 1 briefly touches on some of these methods, and they include density functional theory, ab initio molecular dynamics, and machine learning.Chapter 2 is focused on the Woodward-Hoffmann rules, which dictate "allowed" and "forbidden" stereochemical outcomes in pericyclic reactions. DFT is used to investigate how the use of a transition metal catalyst and stereoelectronic effects can not only allow for a "forbidden" product, but also favor it over the "allowed" product. Chapter 3 then moves to investigate pericyclic reactions in nature as opposed to a lab. DFT is still used as the primary quantum chemistry tool. Chapter 4 involves a change in methods. This chapter still investigates a similar class of reactions, pericyclic reactions, but now the focus is on non-statistical dynamic effects. This dissertation then implements the use of molecular dynamics as a strategy to investigate pericyclic reactions. Specifically, post-transition state bifurcations are investigated in cycloadditions. Finally, chapter 5 uses a similar set of tools as those used in chapter 4, but to tackle a much more complicated (in my opinion) and intensive problem on a different class of molecules. Molecular dynamics are used, but the focus is on non-classical carbocations. This chapter investigates what the relationship is between a different flavor of non-statistical dynamics effects, dynamic matching specifically, and quantum mechanical tunneling. Quasiclassical trajectories are used to gain insight about dynamic matching, but ring-polymer molecular dynamics (RPMD) trajectories are needed to address tunneling questions. RPMD is an expensive method, thus, a machine learning potential was added to the set of tools used.