Rapid X-ray variability arises from regions close to the black hole in a binary system. After a brief introduction, I will highlight a few cases where India's first space observatory - AstroSat's observations and new theoretical formalism has shed light on the processes that lead to such variability. Decades old predictions of General Relativity are now being verified using AstroSat data. In the near future, data from AstroSat and other observatories along with more sophisticated theoretical modelling, is expected to test these predictions in more detail. However, despite these advancements in observational and theoretical techniques, many aspects of these systems remain as cosmic riddles whose explanation would require perhaps ingenious and out of the box ideas.