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Core-collapse theory brings together many facets of high-energy and nuclear astrophysics and the numerical arts to present theorists with one of the most important, yet frustrating, astronomical questions: "What is the mechanism of core-collapse supernova explosions?" A review of all the physics and the fifty-year history involved would soon bury the reader in minutiae that could easily obscure the essential elements of the phenomenon, as we understand it today. Moreover, much remains to be discovered and explained, and a complicated review of an unresolved subject in flux could grow stale fast. Therefore, in this paper I describe what I think are various important facts and perspectives that may have escaped the attention of those interested in this puzzle. Furthermore, I attempt to describe the modern theory's physical underpinnings and briefly summarize the current state of play. In the process, I identify a few myths (as I see them) that have crept into modern discourse. However, there is much more to do and humility in the face of this age-old challenge is clearly the most prudent stance as we seek its eventual resolution.
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