Pancharatnam Lecture

By now gravitational wave observations have established that black holes are ubiquitous in our universe. But what exactly is a black hole? What exactly is it that forms as a result of a gravitational collapse and evaporates due to quantum radiation? The common answer is of course 'horizons'. But the notion of horizons is rather enigmatic For example, an event horizon may be forming and growing in your room in anticipation of a gravitational collapse that may take place a billion years from now! However there are alternative notions that can be used in an effective manner both in the analysis of black hole mergers in classical general relativity as well as the quantum process of black hole evaporation. This account of vexing and fascinating properties of black hole horizons will be presented at a level that should be accessible to to a general Physics and Astronomy audience including research students.