The collapse of the core and the associated supernova explosion mark the end of life of most massive stars, but the mechanism of explosion is poorly understood and perhaps even unknown. Some of its puzzling features were recently observed in the statistics of supernova progenitors, explosion energies, nickel yields, and in the remnant neutron star and black hole mass functions. I will describe my theoretical studies of the supernova explosion mechanism, its dependence on the progenitor star structure, and the connection with observables. I will argue that successful explosions are intertwined with failures in a complex but well-defined pattern that is tied to the pre-collapse structure of the progenitor star. I will also present a new method to extract the supernova parameters from light curves and expansion velocities, and illustrate how to constrain the explosion mechanism in the future.