  The discovery of a pulsar (PSR) in orbit around a black hole (BH) is expected
to provide a superb new probe of relativistic gravity and BH properties. Apart
from a precise mass measurement for the BH, one could expect a clean
verification of the dragging of space-time caused by the BH spin. In order to
measure the quadrupole moment of the BH for testing the no-hair theorem of
general relativity (GR), one has to hope for a sufficiently massive BH. In this
respect, a PSR orbiting the super-massive BH in the center of our Galaxy would
be the ultimate laboratory for gravity tests with PSRs. But even for gravity
theories that predict the same properties for BHs as GR, a PSR-BH system would
constitute an excellent test system, due to the high grade of asymmetry in the
strong field properties of these two components. Here we highlight some of the
potential gravity tests that one could expect from different PSR-BH systems,
utilizing present and future radio telescopes, like FAST and SKA.
