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.