The lives of high-mass stars end with core-collapse supernovae, which distribute energy and chemical elements into the interstellar medium. This process is integral to the Galactic ecosystem, since stars and planets will form from the enriched interstellar medium. Since most supernovae are detected at intergalactic distances, opportunities to examine them in detail are rare. Computer simulations and observations of supernova remnants are frequently employed to study these events and their influence on the universe. I explore the topic of supernovae using a multi-pronged approach, beginning with an examination of the core-collapse supernova engine. The radioisotopes 44Ti and 56Ni, produced in the innermost ejecta, provide a probe of this central engine. Using a three-dimensional supernova simulation with nucleosynthesis post-processing, I examine the production of these isotopes and their thermodynamic histories. Since production of 44Ti is especially sensitive to the explosion conditions, insights can be gained by comparing the model with 44Ti observations from supernova remnant Cassiopeia A. Next, I consider supernova remnants as potential sources of high-energy neutrinos within the Milky Way galaxy. The developing field of neutrino astronomy has yet to identify the origins of the diffuse neutrino flux first detected by the IceCube Neutrino Observatory in 2013. In principle, high-energy Galactic sources like supernova remnants could contribute measurably to this flux. I also consider Galactic open clusters, environments which are rich in supernovae and other energetic phenomena. Statistical analysis finds no evidence of causal association between these objects and the IceCube neutrino events. I conclude with a series of asymmetric three-dimensional supernova models, presented as a comparative analysis of how supernova morphology affects nucleosynthetic yields. Both real supernovae and simulations frequently exhibit aspherical morphologies, but the detailed thermodynamic consequences and the ultimate effects on yields are poorly understood. The simulations include symmetric and bipolar explosion geometries for both 15- and 20-solar-mass progenitor stars. Across the spectrum of models, I show how small changes in the peak temperatures and densities experienced by ejecta can influence the production of notable isotopes such as 44Ti.