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ABSTRACT: The explosion mechanism of core-collapse supernovae - the vibrant neutrino-driven explosion of massive stars - presents an unsolved problem for over half a century, since the earliest simulations by Stirling Colgate in the 1960s. Recent improvements in high-performance computing and neutrino physics have enabled a new generation of multi-dimensional simulations of core-collapse supernovae that produce robust explosions. I will present results of the largest 3D suite of simulations to-date, probing the global behavior of stellar explosion and the dependence on massive star progenitors. I will discuss the joint detectability of correlated neutrinos and gravitational waves from such events, which will illustrate the dynamics of the remnant neutron star, the morphology of the explosion, and global stellar instabilities. Of particular interest and emphasis will be the gravitational wave signatures from both matter and neutrino anisotropies in CCSNe events as probes of the collapse dynamics. These cumulative results galvanize synergistic observational and theoretical forays into core-collapse supernovae as Nature's astrophysical laboratories.