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	Abstract
1	Introduction
2	Basic Notions
	2.1	Isolated horizons
	2.2	Dynamical horizons
3	Area Increase Law
	3.1	Preliminaries
	3.2	Area increase law
	3.3	Energy flux due to gravitational waves
4	Black Hole Mechanics
	4.1	Mechanics of weakly isolated horizons
	4.2	Mechanics of dynamical horizons
	4.3	Passage of dynamical horizons to equilibrium
5	Applications in Numerical Relativity
	5.1	Numerical computation of black hole mass and angular momentum
	5.2	Initial data
	5.3	Black hole multipole moments
	5.4	Waveform extraction
6	Applications in Mathematical Physics
	6.1	Beyond Einstein-Maxwell theory
	6.2	Structure of colored, static black holes
7	Applications in Quantum Gravity
	7.1	Preliminaries
	7.2	Quantum horizon geometry
	7.3	Entropy
8	Outlook
9	Acknowledgements
	References
	Figures
	Footnotes

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