This project aims to develop a comprehensive picture of the explosions of massive stars as core-collapse supernovae using high-end computer simulations. Such explosions come in many varieties and arise from different classes of progenitor stars. This project seeks to thoroughly understand this diversity. It endeavours to provide simulations of supernovae powered by magnetic fields, supernovae that produce black holes, supernovae in binary systems, and the most energetic neutrino-driven supernovae. The project also aspires to better link numerical simulations, observations of supernovae and their remnants, and the nucleosynthesis fingerprints that supernovae have left in the chemical history record of galaxies.