At the end of your return you were asked to enter a phone number. This is optional. If you did, you should have received a text message if your return was accepted or rejected.  An email is also sent to the email you put on your return.  You can log in to your Turbo Tax account an any time to see your status. It usually within 21 days of acceptance if you e-file with direct deposit to receive your refund. 

This article will provide more information on the refund process and timeline. https://blog.turbotax.intuit.com/tax-refunds/wheres-my-tax-refund-how-to-check-your-refund-status-18...  

In order to track your refund, you will need.

Social security number or ITIN.

Your filing status.

Your exact refund amount. 

You can sign back into your account to see the refund amount.  

You can track your refund with the IRS and through Santa Barbara Tax Products Group.

https://taxpayer.sbtpg.com/login

https://www.irs.gov/refunds

That did not answer my question at all; I signed up for alerts and I got a text when my return was accepted. I did not get a text when it was approved or sent and the day I actually received my refund, turbo tax still showed the status as accepted. I was asking why turbo tax didn't keep up with the progress of my return. Even today it still only says accepted.

Turbo Tax will not keep up with the progress of your return. The text message will advise your return is accepted, approved and sent to the IRS. After that you can track your return via the IRS website, not via Turbo Tax. You can use the links above for tracking.