  In this paper, we review our current efforts to test General Relativity in
the strong field regime by studying the reflection spectrum of supermassive
black holes. So far we have analyzed 11 sources with observations of NuSTAR,
Suzaku, Swift, and XMM-Newton. Our results are consistent with general
relativity, according to which the spacetime metric around astrophysical black
holes should be well approximated by the Kerr solution. We discuss the
systematic uncertainties in our model and we present a preliminary study on the
impact of some of them on the measurement of the spacetime metric.
