  We summarize the results of core collapse supernova theory from one-, two-,
and three-dimensional models and provide a snapshot of the field at this time.
We also present results from the "Oak Ridge" group in this context. Studies in
both one and two spatial dimensions define the necessary} physics that must be
included in core collapse supernova models: a general relativistic treatment of
gravity (at least an approximate one), spectral neutrino transport, including
relativistic effects such as gravitational redshift, and a complete set of
neutrino weak interactions that includes state-of-the-art electron capture on
nuclei and energy-exchanging scattering on electrons and nucleons. Whether or
not the necessarily approximate treatment of this physics in current models
that include it is sufficient remains to be determined in the context of future
models that remove the approximations. We summarize the results of the Oak
Ridge group's two-dimensional supernova models. In particular, we demonstrate
that robust neutrino-driven explosions can be obtained. We also demonstrate
that our predictions of the explosion energies and remnant neutron star masses
are in agreement with observations, although a much larger number of models
must be developed before more confident conclusions can be made. We provide
preliminary results from our ongoing three dimensional model with the same
physics. Finally, we speculate on future outcomes and directions.
