  The thermal, spin and magnetic evolution of neutron stars in the old low mass
binaries is first explored. Recycled to very short periods via accretion
torques, the neutron stars lose their magnetism progressively. If accretion
proceeds undisturbed for 100 Myrs these stars can rotate close to break up with
periods far below the minimum observed of 1.558 ms. We investigate their
histories using population synthesis models to show that a tail should exist in
the period distribution below 1.558 ms. The search of these ultrafastly
spinning neutron stars as pulsars can help discriminating among the various
equations of state for nuclear matter, and can shed light into the physics of
binary evolution.
  The evolution of isolated neutron stars in the Galaxy is explored beyond the
pulsar phase. Moving through the tenuous interstellar medium, these old
solitary neutron stars lose their rotational energy. Whether also their
magnetism fades is still a mystery. A population synthesis model has revealed
that only a tiny fraction of them is able to accrete from the interstellar
medium, shining in the X-rays. There is the hope that these solitary stars will
eventually appear as faint sources in the Chandra sky survey. This might give
insight on the long term evolution of the magnetic field in isolated objects.
