When you have a specific chat in context in your Agent Desk, additional details about the chat as well as details about chats you've had with this end-user in the past are available in the panel on the right.

Select the History tab from the panel on the right to view a full listing of all engagements that the specific end-user has had with your business across all channels linked to Chat Desk (most recent at the top). Hovering over any of the chats listed in the History tab brings up a "launch" icon. Click on that icon to open the historic chat (read-only) to view it in more detail.

For more information, see the Chat Desk User Guide.