Previous answers are comprehensive about Joomla Core MVC. As an alternative MVC for Joomla, FOF
What is FOF
FOF (Framework on Framework) is a rapid application development framework for Joomla!. Unlike other frameworks it is not standalone. It extends the Joomla! Platform instead of replacing it, featuring its own forked and extended version of the MVC classes, keeping a strong semblance to the existing Joomla! MVC API. This means that you don't have to relearn writing Joomla! extensions. Instead, you can start being productive from the first day you're using it. Our goal is to always support the officially supported LTS versions of Joomla! and not break backwards compatibility without a clear deprecation and migration path.
FOF is compatible with the database technologies used by Joomla! itself: MySQL, SQL Server (and Windows Azure SQL), PostgreSQL. In most cases you can write a component in one database server technology and have it run on the other database server technologies with minimal or no effort.
FOF is currently used by free and commercial components for Joomla! by an increasing number of developers.