Matrix servers store the conversation history for their local users. The message contents (for e2ee rooms) are e2e-encrypted. The metadata (which user sent it

Matrix servers store the conversation history for their local users. The message contents (for e2ee rooms) are e2e-encrypted. The metadata (which user sent it where and when and to who) is not currently encrypted or obfuscated. We're working on addressing this in the context of P2P matrix (as per https://arewep2pyet.com https://arewep2pyet.com).