As with previous releases, Joomla! provides a unified and easy-to-use framework for delivering content for Web sites of all kinds. To support the changing nature of the Internet and emerging Web technologies, Joomla! required substantial restructuring of its core functionality and we also used this effort to simplify many challenges within the current user interface.
Joomla! 1.5 added many new features. Joomla 1.6 was developed as a major change. It took three years to complete. Since then, the Joomla Team has been adding function on a semi-annual to annual basis. Joomla 1.7 moved to J2.5, and then to J3.x. Currently the stable release is Joomla 3.1.5. This site is running on Joomla 3.1.5.
On August 1st, 2013, The Joomla Project announced the immediate availability of Joomla 3.1.5. This is a security release addressing a critical level security issue. The Production Leadership Team's goal is to continue to provide regular, frequent updates to the Joomla community. You may learn lots more about Joomla! development at the Joomla site. Besides that, Brian Kelly has written seven books about Joomla and these are available for pruchase at www.letsgopublish.com and www.bookhawkers.com
For those with an old Joomla release, the update process is much more simple. Complete instructions are available here. Note that there are now easier and better ways of updating than copying the files with FTP.
Joomla 3.1.5 is the latest version as Joomla is getting more and more powerful. It works on all systems that support PHP and MySQL.