  We discuss the recent efforts to use a sub-class of neutron-star X-ray
transients (the quasi-persistent transients) to probe the properties of
neutron-star crusts and cores. Quasi-persistent X-ray transients experience
accretion episodes lasting years to decades, instead of the usual weeks to
months of ordinary, short-duration transients. These prolonged accretion
episodes should significantly heat the crusts of the neutron stars in these
systems, bringing the crusts out of thermal equilibrium with their neutron-star
cores. When these systems are back in quiescence, i.e. when no more accretion
onto the neutron-star surfaces occurs, then the crusts should thermally radiate
in X-rays, cooling them down until they are again in thermal equilibrium with
the cores. In this chapter we discuss the recent X-ray monitoring campaigns we
performed (using the X-ray satellites Chandra and XMM-Newton) to study several
quasi-persistent neutron-star X-ray transients in their quiescent states. These
observations gave us, for the first time, a detailed look into the cooling
curves of accretion heated neutron-star crusts. In this chapter, we discuss how
these crust cooling curves can provide insight into the structure of neutron
stars.
