Twister has a desktop client which can also serve as a localhost webserver you browse to and get a Twitter-like experience.
The main focus of the project is censorship-resistance [allegedly. No citation given on purpose. Read the source :p]. There's no way to delete anything. Your typos will live forever.
Twisterio.com is a read only web gateway for public twists.
It's unclear who runs the service, so if you're looking for something specific, best is to access it via Tor :)
Example timelines on twisterio:
- Miguel Freitas (author of Twister).
- "NSA Public Relations" (links to related news with humoristic remarks).
- The Intercept (unclear whether a bot or official).