The mechanism for robust explosion of core-collapse supernovae (CCSNe) endures as a scientific mystery for over half a century. 50 years have lapsed since the early works by Sterling Colgate identifying neutrinos as key to reviving a stalled explosion. Novel advances in neutrino physics and high performance computing have likewise revived stalled efforts in CCSNe research. I will present simulations of a series of 2D models whose outcome - explosion or dud - depends sensitively on the progenitor structure, the neutrino-matter microphysics, and macrophysical properties (e.g., rotation and velocity perturbations). I will conclude with recently published results of the first multi-megahour 3D simulation of a CCSN progenitor with detailed microphysics and state of the art neutrino transport. Our model explodes vigorously within 100 milliseconds, and is estimated to accumulate energy at an asymptotic rate of 0.5 Bethe (10^50 erg) over 2 seconds.