Kunena is the leading Joomla forum component. Downloaded more than 5M times in 6 years, Kunena is the only forum/discussion solution for Joomla that is community driven - true open source - public self-help forums, GitHub and documentation Wiki.
The most recent stable release, recommended for production websites running J! 3.4 , is Kunena 4.0.5
Details about Kunena 4.0.5 are contained in the release notes at http://www.kunena.org/docs/Kunena4.0.5Read_Me
For more details about the extent of Kunena features see http://www.kunena.org/docs/Kunena_Features