(not a tech expert, but I’ve been following it for a while, so I hope this is mostly correct)

Bluesky the app is currently the only (major) app running on the ATProtocol. The protocol itself is open source, and it is technically possible to run your own “federated” version (it’s not called that in the ATProto ecosystem, but that’s the rough equivalent in activitypub-speak). The protocol is still being developed, so it’s not as feature-complete as some people are hoping for, but it’s getting there.

techdirt.com/…/some-slightly-biased-thoughts-on-t… for a more professional write-up on the differences, similarities, and criticisms of the major twitter alternatives.