After the pioneer paper by Zeldovich (1964) it was largely recognized that the most spectacular observational appearances of compact stars must occur when they are in a binary system. Indeed, apart from single radiopulsars (Manchester and Taylor, 1977), a large portion of which may have descended from disrupted binaries, the vast majority of compact stars are observed as components of binary systems; it seems that with the present level of observational techniques, black holes can only be discovered in binaries.
At present, there are many excellent reviews describing the current observational status of WD, NS and possible BH candidates in binary systems (see, e.g. Giovannelli, 1991 ; van Paradijs and McClintock, 1993; van den Heuvel, 1994). So here we limit ourselves by briefly sketching out different kinds of presently known binaries that contain compact stars. The list of different types of binary systems with compact stars is presented in Table 1.