  I describe work on two aspects of magnetic field evolution relevant for the
"recycling" scenario for making millisecond radio pulsars. First, many of the
theoretical ideas for bringing about accretion-induced field decay rely on
dissipation of currents in the neutron star crust. I discuss field evolution in
the crust due to the Hall effect, and outline when it dominates Ohmic decay.
This emphasises the importance of understanding the impurity level in the
crust. Second, I briefly discuss the progress that has been made in
understanding the magnetic fields of neutron stars currently accreting matter
in low mass X-ray binaries. In particular, thermonuclear X-ray bursts offer a
promising probe of the magnetic field of these neutron stars.
