Neutron stars possess the strongest gravitational fields
among stellar objects in the Universe that are not surrounded by a horizon.
This causes the emission from their surfaces to be strongly lensed and
deformed. Two upcoming space X-ray missions, ESA's LOFT and NASA's NICER, aim
to use observations of lightcurves from spinning neutron stars to map their
gravitational fields as well as measure their masses and radii. In this talk, I
will discuss some unexpected strong-field phenomena that affect gravitational
lensing in the vicinity of neutron stars. I will then show how we can use these
phenomena to measure strong-field frame dragging and break degeneracies in the
measured neutron-star masses and radii.