You can run your own 1999 server, or you can create a site on someone else's server.
The server software is open source, MIT License. The editor is not open source.
On the back-end there is no database, just folder structures of JSON, HTML, RSS and OPML files.
The pages are "live" meaning they display all updates instantaneously. This makes 1999 ideal for liveblogging applications, and since it's the first blogging software to have this live connection it probably will inspire some wholly new applications. We use standard web technology for this feature.
All users have full access to all the underlying data of their blogs. There's a single command in the Main menu for every blog that downloads the full JSON representation of all the data for their blog, exactly as it's stored on the server.
We use Twitter for identity. It's a very practical system, and easy and quick for server operators to hook into. However the data is stored on your server not Twitter's.