  Dynamical interactions that take place between objects in dense stellar
systems lead to frequent formation of exotic stellar objects, unusual binaries,
and systems of higher multiplicity. They are most important for the formation
of binaries with neutron stars and black holes, which are usually
observationally revealed in mass-transferring binaries. Here we review the
current understanding of compact object's retention, of the metallicity
dependence on the formation of low-mass X-ray binaries with neutron stars, and
how mass-transferring binaries with a black hole and a white dwarf can be
formed. We discuss as well one old unsolved puzzle and two new puzzles posed by
recent observations: what descendants do ultra-compact X-ray binaries produce,
how are very compact triples formed, and how can black hole low-mass X-ray
binaries acquire non-degenerate companions?
