Synapse is an open-source Matrix homeserver written and maintained by Element. Matrix is an open standard for decentralised real-time communication: users register with a provider, and people on different providers can still message one another. A homeserver such as Synapse stores accounts and message history and federates with other servers. Synapse offers an admin API, pluggable modules, optional single sign-on and worker processes for scaling. It can be installed standalone or deployed through Element Server Suite on Kubernetes, either self-hosted or fully managed by Element.
Synapse is dual-licensed: under the AGPL, or under a paid Element Commercial License. The Matrix standard itself is stewarded by the Matrix.org Foundation, a non-profit UK community interest company. Because anyone can run a homeserver, where data resides depends on where you host it: a European organisation can operate Synapse on its own infrastructure in the EU and control retention and access. Element provides support only with a subscription. The sources reviewed do not state where Element's managed hosting is located.