For approximately half a century, core-collapse supernovae have posed a vexing puzzle for theorists despite being a major ingredient (and uncertainty) in fields ranging from stellar and galaxy evolution to the interstellar medium. Historically, advances in core-collapse theory have been linked to advances in computing power and software. Supernovae are inherently multi-dimensional objects in which neutrino transport, gravity, hydrodynamic instabilities and convection play important roles. Three-dimensional simulations incorporating sufficient physical fidelity require extensive high-performance computing resources and codes efficient enough to use the associated architecture. In this talk, I will highlight recent advances in the field. In particular, I will discuss the dependence of spatial dimension on the viability of the neutrino mechanism and the origin of pulsar kicks.
