Black Holes and Quantum Stars: Observer's Paradise?

Einstein's theory of gravity predicts the existence of Black Holes and Space-time Singularities. The Singularities may be hidden within a Black Hole or visible to faraway observers in the Universe, also called Naked Singularities. The Black Holes and Naked Singularities arise from gravitational collapse of massive stars, and we discuss the current efforts to make a direct observational detection of these entities. Quantum gravity effects dominate near naked singularities, that may be called long or short-lived 'Quantum Stars'. These potentially offer an exciting opportunity to test the quantum theories of gravity, or the Unification of Physics. The connection to new observational missions such as the Event Horizon Telescope, Gravitational Waves, TMT, and others are pointed out, and recent emerging theoretical developments are indicated.