What can we learn about black-hole formation from black-hole X-ray binaries?

I discuss the effect of the formation of a black hole on a (close) binary and show some of the current constraints that the observed properties of black hole X-ray binaries put on the formation of black holes. In particular I discuss the evidence for and against asymmetric kicks imparted on the black hole at formation and find contradicting answers, as there seems to be evidence for kick for individual systems and from the Galactic $z$-distribution of black hole X-ray binaries, but not from their line-of-sight velocities.