  Over the past three decades, black holes have played an important role in
quantum gravity, mathematical physics, numerical relativity and gravitational
wave phenomenology. However, conceptual settings and mathematical models used
to discuss them have varied considerably from one area to another. Over the
last five years a new, quasi-local framework was introduced to analyze diverse
facets of black holes in a unified manner. In this framework, evolving black
holes are modeled by dynamical horizons and black holes in equilibrium by
isolated horizons. We review basic properties of these horizons and summarize
applications to mathematical physics, numerical relativity and quantum gravity.
This paradigm has led to significant generalizations of several results in
black hole physics. Specifically, it has introduced a more physical setting for
black hole thermodynamics and for black hole entropy calculations in quantum
gravity; suggested a phenomenological model for hairy black holes; provided
novel techniques to extract physics from numerical simulations; and led to new
laws governing the dynamics of black holes in exact general relativity.
