Accreting black holes are powerful sources of radiation. The conversion of gravitational energy into radiation is thought to take place in an accretion disk-corona system just outside the black hole. In this system, thermal accretion disk photons are upscattered in a corona of hot electrons situated above the accretion disk, producing X-rays. The nature of this Comptonizing corona remains a key open question in astrophysics. I will discuss recent INTEGRAL and NuSTAR results on galactic black hole binary and AGN coronae.