The current status of the problem of whether neutron stars can form, in close binary systems, by accretion-induced collapse (AIC) of white dwarfs is examined. We find that, in principle, both initially cold C+O white dwarfs in the high-mass tail of their mass distribution in binaries and O+Ne+Mg white dwarfs can produce neutron stars. Which fractions of neutron stars in different types of binaries (or descendants from binaries) might originate from this process remains uncertain.