The chatbox and the inbox both have read indicators in the chat log so that visitor and the team know when a reply is likely to have been seen.
These are the same types of indicator you will be familiar with in other services.
However, there is a slightly different behaviour for the visitor after they send a new message. For a conversation that still has a pending status the visitor will still see that the conversation is unread. This essentially keeps you hidden from view giving operators time to evaluate the conversation before responding.
The same applies to operators that have not yet "entered" the conversation by adding their own reply.
If a conversation is pending, all you have to do is send your first reply and the status will change automatically.
When the chatbot engages with a conversation it will also open and update read indicators appropriately. This is due to the bot behaving as an operator in the chat.