Operate\s email notification system is based upon the Two-way Email feature, which allows you to communicate with your customers through your own personal email whilst having the ability to keep track of all correspondence in Operate as well.
The emails that come through two-way email are being stored in your inbox, which you can access by clicking the envelope icon near your profile picture.
This section contains a list of all messages coming through two-way email. When a new message arrives, you will see the number of unread email increase on the envelope icon.
This section is global and only contains a list of individual messages, not conversations. You can follow the conversation by opening the message - where you can also send a reply back to the customer. This reply will be routed through to your personal email, using the two-way email system.
All of the messages found here can be either deleted (using the "x" sign for individual messages or the "Delete" button for multiple entries); or exported as .csv for use in third party applications.