The state of interrelations between observations and theoretical interpretations are different for different groups of compact binaries. Such cataclysmic variables as novae stars have been observed for centuries, their lower-amplitude cousins (including AM CVn-type stars) for decades, and their origin and evolution found their theoretical explanation after the role of common envelopes and gravitational waves radiation and magnetic braking were recognized [301, 302, 417, 435]. At present, about 2,000 CVs are known; see the online catalogue by Downes et al.  at .
More than 600 of them have measured orbital periods; see the online catalogue by Kolb and Ritter  at .
In particular, there are at present 17 confirmed AM CVn-stars with measured or estimated periods and two more candidate systems; see the lists and references in [273, 390] and .
Ultracompact X-ray binaries were discovered with the advent of the X-ray astronomy era in the late 1960s and may be found in the first published catalogues of X-ray sources (see for instance ). Their detailed optical investigation became possible only with 8 m-class telescopes. Currently, 12 UCXB systems with measured or suspected periods are known plus six candidates; six of the known systems reside in globular clusters (see lists and references in [278, 20]). Contrary to cataclysmic binaries, the place of UCXBs in the scenarios of evolution of close binaries, their origin and evolution were studied already before optical identification [418, 341, 411].
Unlike CVs and UCXBs, the existence of close detached white dwarfs (DDs) was first deduced from the analysis of scenarios for the evolution of close binaries [443, 417, 418, 162, 444]. Since it was also inferred that DDs may be precursors of SNe Ia, this theoretical prediction stimulated optical surveys for DDs and the first of them was detected in 1988 by Saffer, Liebert, and Olszewski . However, a series of surveys for DDs performed over a decade [353, 42, 109, 250, 364] resulted in only about a dozen of definite detections .
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