The fuzzball proposal for black holes

The fuzzball proposal states that associated with a black hole of entropy S there are exp S horizon-free non-singular solutions that asymptotically look like the black hole but generically differ from the black hole up to the horizon scale. These solutions, the fuzzballs, are considered to be the black hole microstates while the original black hole represents the average description of the system. The purpose of this report is to review current evidence for the fuzzball proposal, emphasizing the use of AdS/CFT methods in developing and testing the proposal. In particular, we discuss the status of the proposal for 2 and 3 charge black holes in the D1-D5 system, presenting new derivations and streamlining the discussion of their properties. Results to date support the fuzzball proposal but further progress is likely to require going beyond the supergravity approximation and sharpening the definition of a "stringy fuzzball". We outline how the fuzzball proposal could resolve longstanding issues in black hole physics, such as Hawking radiation and information loss. Our emphasis throughout is on connecting different developments and identifying open problems and directions for future research.