  In the Loop Quantum Gravity, black holes (or even more general Isolated
Horizons) are described by a SU(2) Chern-Simons theory. There is an equivalent
formulation of the horizon degrees of freedom in terms of a U(1) gauge theory
which is just a gauged fixed version of the SU(2) theory. These developments
will be surveyed here. Quantum theory based on either formulation can be used
to count the horizon micro-states associated with quantum geometry fluctuations
and from this the micro-canonical entropy can be obtained. We shall review the
computation in SU(2) formulation. Leading term in the entropy is proportional
to horizon area with a coefficient depending on the Barbero-Immirzi parameter
which is fixed by matching this result with the Bekenstein-Hawking formula.
Remarkably there are corrections beyond the area term, the leading one is
logarithm of the horizon area with a definite coefficient -3/2, a result which
is more than a decade old now. How the same results are obtained in the
equivalent U(1) framework will also be indicated. Over years, this entropy
formula has also been arrived at from a variety of other perspectives. In
particular, entropy of BTZ black holes in three dimensional gravity exhibits
the same logarithmic correction. Even in the String Theory, many black hole
models are known to possess such properties. This suggests a possible universal
nature of this logarithmic correction.
