A black hole can swallow matter, and quantum theory says information about physical states should not simply vanish. Hawking’s calculation of black-hole radiation exposed a conflict between that expectation and gravity’s most extreme objects.
The paradox is theoretical, not evidence that black holes break known laws in an observed experiment. General relativity describes gravity and black-hole horizons well in many settings; quantum mechanics describes matter at small scales. A complete theory combining them is still missing.
Mathematical work on quantum entanglement and black-hole evaporation has made significant progress, including ways to recover information in idealized models. The remaining challenge is to understand, in a full and physically realistic account, how information is encoded in the outgoing radiation and how spacetime itself behaves at the deepest levels.