  In this contribution we discuss how neutron stars are produced and retained
in globular clusters, outlining the most important dynamical channels and
evolutionary events that affect thepopulation of mass-transferring binaries
with neutron stars and result in the formation of recycled pulsars. We confirm
the importance of electron-capture supernovae in globular clusters as the major
supplier of retained neutron stars.By comparing the observed millisecond pulsar
population and the results obtained from simulations, we discuss several
constraints on the evolution of mass-transferring systems.In particular, we
find that in our cluster model the following mass-gaining events create
populations of MSPs that do not match the observations (with respect to binary
periods and companion masses or the number of produced systems) and therefore
likely do not lead to NSs spun up to millisecond periods: (i) accretion during
a common envelope event with a NS formed through accretion-induced collapse,
and (ii) mass transfer from a WD donor. By restricting ourselves to the
evolutionary and dynamical paths that most likely lead to neutron star
recycling, we obtain good agreement between our models and the numbers and
characteristics of observed millisecond pulsars in the clusters Terzan 5 and 47
Tuc.
