You can view chats from the Chat app filter pane.
There are inbuilt filters for open (active) chats and ended chats.
The Open Chats section shows current active chats:
Even if you are signed out of chat, you can click on open chats to accept them.
The Ended Chat section shows:
When you view ended chats in the content pane, there is a Create ticket button in the Person section of the chat record. This creates a ticket linked to the chat.
You can use this to quickly open a ticket linked to a missed chat and maintain communication with the user.