Efforts to uncover the explosion mechanism of core collapse supernovae and to understand all of their associated phenomena have been ongoing for nearly four decades. Despite this, our theoretical understanding of these cosmic events remains limited; two- and three-dimensional modeling of these events is in its infancy. Most of the modeling efforts over the past four decades have, by necessity, been constrained to spherical symmetry, with the first two-dimensional, albeit simplified, models appearing only during the last decade. Simulations to understand the complex interplay between the turbulent stellar core fluid flow, its magnetic fields, the neutrinos produced in and emanating from the proto-neutron star, the stellar core rotation, and the strong gravitational fields have yet to be performed. Only subsets of these fundamental ingredients have been included in the models thus far, often with approximation.The purpose of this volume is to identify the outstanding issues that remain in order to come to a complete understanding of these important astrophysical events. As the book focuses on open issues rather than the current state of the art in the field ? although the latter will certainly be discussed ? it will remain relevant for some time.