  General relativity is one of the pillars of modern physics. For decades, the
theory has been mainly tested in the weak field regime with experiments in the
Solar System and radio observations of binary pulsars. Until 2015, the strong
field regime was almost completely unexplored. Thanks to new observational
facilities, the situation has dramatically changed in the last few years. Today
we have gravitational wave data of the coalesce of stellar-mass compact objects
from the LIGO-Virgo-KAGRA Collaboration, images at mm wavelengths of the
supermassive black holes in M87$^*$ and SgrA$^*$ from the Event Horizon
Telescope Collaboration, and X-ray data of accreting compact objects from a
number of X-ray missions. Gravitational wave tests and black hole imaging tests
are certainly more popular and are discussed in other articles of this Special
Issue. The aim of the present manuscript is to provide a pedagogical review on
X-ray tests of general relativity with black holes and to compare this kind of
tests with those possible with gravitational wave data and black hole imaging.
