A general scheme of evolution of close binaries is outlined. Many types of observed systems are classified according to their evolutionary status. Present theory can account reasonably well for the mass transfer between the two components. There is no satisfactory theory of mass and angular momentum loss from binary (as well as single) stars. Most close binaries sooner or later should develop extended common envelopes. A loss of a common envelope may remove a large fraction of mass and most of angular momentum from a binary, and leave as a remnant a very short period and highly evolved system. Binary nuclei of planetary nebulae, cataclysmic variables and some X-ray binaries are produced this way.
I shall present here a picture of the evolution of close binary systems (CBS) as it is understood now. This is not intended to be a review, and no attempt has been made to make the list of references complete. Usually I shall refer the first paper on a given subject and/or one of the recent ones, where a large number of other references can be found. There are many reviews and proceedings of various symposia that deal with close binaries. Here are some: Annual Review of Astronomy and Astrophysics (9, 183, 14, 119, 15, 127, 16, 171, 241), IAU Symposia No. 73, 83, 88, IAU Colloquia No. 42, 46, 53. I shall try to emphasize what is known and what is not known, and how various observed systems fit into the theoretical evolutionary scheme. Because of my background I shall give more references to theoretical papers. Nevertheless, I am convinced that it was the theory of close binaries that was guided in its development by the observations, not other way around. In fact the theory predicted very few new phenomena and very few new types of binaries. But it managed to account, at least qualitatively, for the major evolutionary processes, and made it possible to arrange the observed systems into the evolutionary sequences.