Vaultwarden is a self-hostable server that implements the Bitwarden client API, so the official Bitwarden apps and extensions can connect to it. The project was formerly known as bitwarden_rs. It is written in Rust, and the recommended way to run it is as a container image, available from ghcr.io, Docker Hub and quay.io. The web vault requires HTTPS, for which the project suggests a reverse proxy. It is aimed at anyone who wants to run a password manager for themselves, a team or an organisation on their own infrastructure.
Vaultwarden is open source under the AGPL-3.0 licence and is maintained by an independent community around its developer, dani-garcia. The project states explicitly that it is not associated with Bitwarden or Bitwarden, Inc. No vendor hosts the service: you run the server yourself and so decide where the data is located, for example in a European data centre or on-premises. In return, administration, backups, security and updates rest entirely with your own organisation.