Joist can deliver your estimates and invoices via email, but it is not an email application like Gmail or Yahoo or a program you might have running on your phone or computer.
There is no inbox or sent mail section. If a client replies to an email you sent from Joist, the reply will be delivered to the inbox of whichever email address you have associated with your Joist account.
If you would like to keep a copy of the email you send to your client, be sure to turn on the Send me a copy option on the email sending screen. That way, the same email will be delivered to the inbox of whichever email address you have associated with your Joist account.