ICANN has recently approved IDNs in 19 countries .The most recent approved IDNs are China HongKong, China Taiwan, Sri Lanka, Qatar, Thailand and Tunisia.

This is just a preliminary stage.However,it seems that the string review is the most difficult stage.
Other IDNs that have passed the ICANN preliminary stage are :
Bangladesh
Egypt
Palestinian Territory
Russian Federation
Saudi Arabia
Sri Lanka
United Arab Emirates

IDNs introduction:

An internationalized domain name (IDN) is an Internet domain name that contains at least one label that is displayed in software applications, in whole or in part, in a language-specific script or alphabet, such as Chinese, Russian or the Latin-based languages with diacritics, such as French. These writing systems are encoded by computers in multi-byte Unicode. Internationalized domain names are stored in the Domain Name System as ASCII strings using Punycode transcription.

The Domain Name System, which performs a lookup service to translate user-friendly names into network addresses for locating Internet resources, is restricted to the use of ASCII characters, a technical limitation that initially set the standard for acceptable domain names. The internationalization of domain names is a technical solution to translate names written in language-native scripts into an ASCII text representation that is compatible with the Domain Name System. Internationalized domain names can only be used with applications that are specifically designed for such use, and they require no changes in the infrastructure of the Internet.