  The ultra-relativistic heavy-ion programs at the Relativistic Heavy Ion
Collider and the Large Hadron Collider have evolved into a phase of
quantitative studies of Quantum Chromodynamics at very high temperatures. The
charm and bottom hadron production offer unique insights into the remarkable
transport properties and the microscopic structure of the Quark-Gluon Plasma
(QGP) created in these collisions. Heavy quarks, due to their large masses,
undergo Brownian motion at low momentum, provide a window on hadronization
mechanisms at intermediate momenta, and are expected to merge into a
radiative-energy loss regime at high momentum. We review recent experimental
and theoretical achievements on measuring a variety of heavy-flavor
observables, characterizing the different regimes in momentum, extracting
pertinent transport coefficients and deducing implications for the "inner
workings" of the QGP medium.
