Accretion disks around black holes are the power source behind many luminous and powerful astrophysical systems such as X-ray binaries and active galactic nuclei. The well-known thin disk model does a good job of explaining many accreting black hole systems, but the model is limited to sub-Eddington accretion rates. Can a black hole accrete at a super-Eddington rate? If yes, do we observe such systems, and do they have unique observational signatures? Thanks to advances in numerical simulations, progress is being made on answering some of these questions. The talk will review our current understanding of the field.