Evolution of X-ray binaries: Achievements and advances

Three recent developments in the field of formation and evolution of neutron stars and black holes in binaries are addressed:
• The finding that there is a class of neutron stars, formed in interacting binaries, that do not receive kick velocities in their birth events. This finding is particularly important for our understanding of the formation – and formation rates – of double neutron stars. It is argued that these low-kick neutron stars, which tend to have low masses, are formed by a different physical mechanism than the neutron stars that receive large kick velocities at birth.
• The occurrence of velocity kicks in the formation events of stellar black holes.
• The nature of the companions of millisecond X-ray pulsars.