  The corona is a key component of most luminous accreting black holes,
carrying 5 - 30 % of the power and in non-jetted Active Galactic Nuclei (AGN),
creating all the X-ray emission above $\simeq 1-2$ keV. Its emission
illuminates the inner accretion disc, creating the atomic line-rich reflection
spectrum used to diagnose and map the accretion flow and measure black hole
spin. The corona is likely powered magnetically by the strong differential
rotation of the accretion disc and it may be intimately related to relativistic
jets. Recent work shows that many black hole coronae may be dominated by
electron-positron pairs produced by photon-photon collisions in the compact
coronal environment. Despite the corona being an integral component of AGN and
black hole binary systems, much is still unknown about the nature of the
corona, such as its geometry, location, and the physical mechanisms powering
the emission. In this white paper we explore our current understanding of
coronal properties, such as its temperature, obtained from measurements with
existing hard X-ray telescopes such as NuSTAR, and discuss important questions
to be addressed in the coming decade surrounding the nature of the corona. Hard
X-ray observations will continue to dispel the mystery of coronae and open up
this part of the quasar engine to full understanding.
