Matrix is an open standard, defining simple HTTP APIs so that devs can easily write their own clients, bots, bridges or servers. You're not locked into a specific set of implementations.

Matrix is decentralized, there's no one central point that the information goes through and so no once central point of failure or control.

Matrix has bridges to IRC (freenode, moznet, oftc, snoonet etc), Slack, Gitter, Rocket.Chat, XMPP, SMS, SIP and others. The point is to 'matrix' all the different networks out there into one single decentralised network.

Matrix is designed to support Instant Messaging, VoIP/WebRTC signalling (voice and video) and Internet of Things communication.

Which can be found here.

Matrix is designed to support Instant Messaging, VoIP/WebRTC signalling and Internet of Things communication and allows cross-communication between those services. Meaning one person could be using IRC and another Slack for IMs, or one person could be using Skype and another Google Hangouts for videoconferencing.

Riot.im is the easiest way to use Matrix, with great clients for Web, iOS and Android (and Fdroid).

Matrix aims to "provide an analogous ecosystem to email - one where you can communicate with pretty much anyone, without caring what app or server they are using" using a neutral identity system.

Riot.im includes an app store with integrations for Github, JIRA, Jenkins, Giphy etc - and anyone can add more via Matrix.