Common envelope: the progress and the pitfalls

The common envelope event is one of the most important and uncertain evolutionary stages that lead to formation of compact binaries. While the problem is almost 30 years old, its theoretical foundation did not progress much from the first proposed consideration. For many years, the simple estimate provided by \alpha \lambda-formalism has been intensively used by population synthesis studies and, not surprisingly, frequently contradicted observations. In recent years, the advancements in our studies of stellar structure, progress of the numerical techniques for hydrodynamical simulations as well as increase of the computer power and new observations started to bring improvements to our understanding of the common envelope phase. We review main physical processes taking place during the common envelope phase from the theoretical point of view and how they affect the values of classical formal parameters. In particular, we discuss the energy budget problem -- what are the energy sources, sinks and what is the condition for the envelope to disperse, as well as the importance of choosing the definition of the remnant core to the common envelope outcome.