  We present a first-principles derivation of the main results of the Kerr/CFT
correspondence and its extensions using only tools from gravity and quantum
field theory. Firstly, we review properties of extremal black holes with in
particular the construction of an asymptotic Virasoro symmetry in the
near-horizon limit. The entropy of extremal spinning or charged black holes is
shown to match with a chiral half of Cardy's formula. Secondly, we show how a
thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the
dynamics of near-superradiant probes around near-extremal black holes in the
semi-classical limit. Thirdly, we review the hidden conformal symmetries of
asymptotically-flat black holes away from extremality and present how the
non-extremal entropy can be matched with Cardy's formula. We follow an
effective field theory approach and consider the Kerr-Newman black hole and its
generalizations in various supergravity theories. The interpretation of these
results by deformed dual conformal field theories is discussed and contrasted
with properties of standard 2-dimensional CFTs. We conclude with a list of open
problems.
