Neutron stars in globular clusters can be detected as low-mass X-ray binaries or as millisecond pulsars. In my talk I will review our current knowledge about dynamical channels and evolutionary events in life of mass-transferring binaries with neutron stars which could result in the formation of recycled pulsars, most recent progress in the field, how our theoretical findings are linked with the observations and what further constraints on theoretical studies of binary evolution it gives us.