Slack Bridge allows you to mirror chat to and from Slack within Minecraft. There are still a lot of things that could be improved, but the basic functionality is all present. Users joining Minecraft and getting achievements are also sent to Slack:
Features
Allows to connect to one or more slack teams
Allows to configure which channels to mirror messages to and from
Full 2-way synchronization of messages to and from Slack and Minecraft Chat
Currently missing (and/or planned)
Better handling of emojis
React to Slack user presence changes
Allow Minecraft users to see who's in the Slack chat
Allow Slack users to see who's online in Minecraft
Allow Slack users to authenticate as Minecraft users, so that messages sent from Slack user thefoo can be shown in Minecraft as being sent from Minecraft user FooTheUltimate and vice versa.
More fine-grained control of what to send to Slack (user logged in/out, achievements, etc.)
Handling of a lot of Slack events that are currently just silently ignored (like message-reactions)
