String theory gives a consistent theory of quantum gravity, so we can ask about the nature of black hole microstates in this theory. Studies of extremal and near-extremal microstates indicate that these microstates do not have a traditional horizon, which would have no data about the microstate in its vicinity. Instead, the information of the microstate is distributed throughout a horizon sized quantum `fuzzball'. If this picture holds for all microstates then it would resolve the information paradox. We review recent progress in the area, including some results on non-extremal states. We also discuss some conjectures about black hole dynamics suggested by the structure of fuzzballs.