The common envelope phase of binary star evolution plays a central role in many evolutionary pathways leading to the formation of compact objects in short period systems. Using three dimensional hydrodynamical computations, we review the major features of this evolutionary phase, focusing on the conditions that lead to the successful ejection of the envelope and, hence, survival of the system as a post common envelope binary. Future hydrodynamical calculations at high spatial resolution are required to delineate the regime in parameter space for which systems survive as compact binary systems from those for which the two components of the system merge into a single rapidly rotating star. Recent algorithmic developments will facilitate the attainment of this goal.
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