  Einstein's theory of general relativity was proposed over 100 years ago and
has successfully passed a large number of observational tests in the weak field
regime. However, the strong field regime is largely unexplored, and there are
many modified and alternative theories that have the same predictions as
Einstein's gravity for weak fields and present deviations when gravity becomes
strong. RELXILL_NK is the first relativistic reflection model for probing the
spacetime metric in the vicinity of astrophysical black holes and testing
Einstein's gravity in the strong field regime. Here we present our current
constraints on possible deviations from Einstein's gravity obtained from the
black holes in 1H0707-495, Ark 564, GX 339-4, and GS 1354-645.
