The possible way offered by Bose-Einstein condensation for investigating the quantum world made much progress for exciton condensation in semiconductor nanometer structures. In particular,the lifetime of indirect excitons has been dramatically improved by more than two orders of magnitudes by using the spatial separation of electrons and holes that form excitons in coupled quantum wells. This allows the excitons to be cooled down below 1 K and the condensation or highly degenerate states of excitons to be realized experimentally.Phenomena in the cold exciton gases such as condensation,pattern formation and macroscopically ordered exciton states were reviewed. Understanding the formation mechanisms of these degenerate exciton systems can open new opportunities for the last realization of exciton Bose-Einstein condensation in semiconductor nanometer structures.