The black hole information paradox is a poorly understood problem in physics. Hawking's argument is often considered flawed, but the author shows that small quantum corrections to Hawking's calculation cannot resolve the paradox. The paradox arises because the radiation from a black hole is entangled with the hole, and this entanglement cannot be removed by quantum corrections. The author formulates Hawking's argument as a theorem: assuming traditional physics at the horizon and locality, one is forced into mixed states or remnants. The author also argues that the AdS/CFT duality cannot explain away the paradox. Recent results on black hole quantum physics show that black holes have a 'fuzzball' structure, which resolves the information paradox by providing a nontrivial microstate structure. This structure allows for a qualitative understanding of how classical intuition breaks down in black hole physics. The author then discusses the 'solar system limit' and the 'niceness conditions' N that are essential for semiclassical physics. These conditions include requirements on the curvature of spacetime, the extrinsic curvature of spacelike slices, and the behavior of matter. The author then describes the quantum process of interest, including pair creation and the entanglement of radiation with the black hole. The author also discusses the evolution of spacelike slices and the stretching of spacetime near the black hole horizon. The author shows that the Hawking radiation process leads to entanglement between the radiation and the black hole, which cannot be removed by small corrections. The author then discusses the stability of the Hawking state and shows that small corrections do not change the conclusion that the black hole must either emit a mixed state or leave a remnant. The author concludes that the information paradox is a deep problem that requires a fundamental change in our understanding of quantum gravity.The black hole information paradox is a poorly understood problem in physics. Hawking's argument is often considered flawed, but the author shows that small quantum corrections to Hawking's calculation cannot resolve the paradox. The paradox arises because the radiation from a black hole is entangled with the hole, and this entanglement cannot be removed by quantum corrections. The author formulates Hawking's argument as a theorem: assuming traditional physics at the horizon and locality, one is forced into mixed states or remnants. The author also argues that the AdS/CFT duality cannot explain away the paradox. Recent results on black hole quantum physics show that black holes have a 'fuzzball' structure, which resolves the information paradox by providing a nontrivial microstate structure. This structure allows for a qualitative understanding of how classical intuition breaks down in black hole physics. The author then discusses the 'solar system limit' and the 'niceness conditions' N that are essential for semiclassical physics. These conditions include requirements on the curvature of spacetime, the extrinsic curvature of spacelike slices, and the behavior of matter. The author then describes the quantum process of interest, including pair creation and the entanglement of radiation with the black hole. The author also discusses the evolution of spacelike slices and the stretching of spacetime near the black hole horizon. The author shows that the Hawking radiation process leads to entanglement between the radiation and the black hole, which cannot be removed by small corrections. The author then discusses the stability of the Hawking state and shows that small corrections do not change the conclusion that the black hole must either emit a mixed state or leave a remnant. The author concludes that the information paradox is a deep problem that requires a fundamental change in our understanding of quantum gravity.