What are XMPP and Matrix and what makes them special? XMPP and Matrix are two decentralized and federated free sofware projects for chat, including true end-to-end encrypted chat. Users can either install the software on their own server if they want, but they can also easily register on any public server—both allow any XMPP or Matrix user to talk to users on their server or on any other one. In essence, it works like email: you might have an email account on a different site than your friend, but all accounts on all sites can communicate.