Theoretical models and simulations that describe chemical systems at the quantum mechanical level of electrons and nuclei have become essential components supporting experimental chemistry. The use of adequately accurate quantum mechanical simulations can help guide experiments in the laboratory, or assist in the interpretation of experimental results. Density functional theory (DFT) in particular has become the most widely used method in electronic structure due to generally good performance for a moderate computational cost. The work in this thesis primarily involves the application of DFT and other electronic structure methods to explore chemical processes in the realms of astrochemistry and combustion chemistry. For all studies, we employ the generally accurate $\omega$B97X-V density functional, and in some cases bolster our results using coupled-cluster methods with singles, doubles and perturbative triples correction (CCSD(T)). In Chapter 2, we characterize the cation, anion, and radical isomers of \ch{C4H4N}, as well as reaction pathways that may lead to these isomers. Small, nitrogenated species such as \ch{C4H4N} may be important precursors to pre-biotic molecules formed in non-Earth environments such as the atmosphere of Titan, a moon of Saturn. In Chapter 3, we investigate more Earthly processes that may lead to incipient soot particles during incomplete combustion reactions of hydrocarbons. Specifically, rate constants for hydrogen ejection reactions are calculated and reaction sequences are modeled for a suite of polycyclic aromatic hydrocarbons that are postulated to be quite important in radical-chain reaction pathways leading to soot. In Chapter 4, we return to the interstellar medium, this time exploring surface reactions on cold, icy grains. To this end, we explore the optimized complex geometries and binding energies of astrochemically relevant neutral closed-shell, neutral open-shell, anionic and cationic small molecules to water clusters of up to four waters. Such quantities are important for constructing accurate models of interstellar reaction chemistry, where cold grains play an important role in the production and observed abundances of gas-phase species.