A Simple answer is that you can use any data storage format, from standard defined, to database (which generally involved a protocol), even a bespoke file-format.
There are trade-offs for every choice you make in IT, and certainly websites are no different. In the early 2000's file-based forum systems were popular as it allows anyone with limited technical ability to edit pages and posts. Completely static sites swiftly become unmanageable and content does not benefit from upgrades to the site user-interface; however the site if coded correctly can simply be moved to a sub-directory, or ripped into the new design. CMS's and dynamic systems bring with them their own set of problems, namely that there does not yet exist a widely adopted standard for data storage amongst them; that they often rely on third-party plugins to provide features between design styles (despite their documentation advocating for separation of function & form).
In 2016, it's pretty uncommon not to use a standard storage mechanism, such as a *SQL RDBMS; although static site generators such as Jekyll (powers a lot of GitHub pages); and independent players such as October CMS still provision for static file-based storage.
My personal preference is to use an *SQL enabled RDBMS, it provides me syntax that is standardised at least at the vendor level, familiar and powerful syntax, but unlike a lot of people I don't think this is the only way, and in most cases would advocate for using a site-generator to save parts that don't have to be dynamic to a static store as this is the cheapest way to live on the web.
TLDR; it's up to you, SQL & RDBMS backed are popular.