All unread messages—including alerts, invitations, and requests—are considered "new" until you've viewed them. If you don't see any recently received messages in your Inbox, scroll down to check for any older messages you have not yet opened, and make sure to check under the Notifications tab as well. Unread messages and notifications will have an orange dot next to them.
In some cases, you may need to log out and then log back in before your inbox reflects that all messages have been read.