Black holes are among the most extreme objects in the universe — regions where gravity wins so completely that not even light escapes. But what happens nearby, and how do we study something invisible? In this talk, I will take you on a journey through six decades of black hole astronomy, told through X-ray observations of Galactic X-ray binaries - stellar-mass black holes caught devouring their companion stars. We will trace the story from the pioneering discoveries of early X-ray astronomy through the transformative Rossi X-ray Timing Explorer (RXTE). I will then share some of what India's own AstroSat satellite has been teaching us a genuinely exciting chapter in which Indian astronomers have moved to the front row of this field.

Yet here is the humbling truth: after six decades of intensive study, a definitive physical picture of the black hole environment remains stubbornly out of reach. I argue that hard X-ray and soft gamma-ray observations - a window into the geometry and physics of the innermost regions - are emerging as a crucial key to unlocking these mysteries. AstroSat has already given us some hints by measuring X-ray polarisation in black hole sources above 100 keV. I will discuss what this tells us, and close with a look at some speculative but tantalising future hard X-ray experiments that could, finally, bring us closer to understanding what nature is doing right at the edge of a black hole.