I filed my returns on time but have not received my refund. I have a email from the federal saying they have my return.

[Critter-3]

If you efiled, double-check to be sure the returns were efiled successfully and accepted.
If you used Online TurboTax, you can sign into your Online Account and check the efile status at the Tax Home.

If that showed it was accepted, you can use the "Where's My Refund" tool at the IRS website below to monitor the status of your Federal refund.     What is displayed there?
https://www.irs.gov/Refunds

NOTE:

• When using that tool,  be sure to enter the correct SSN and filing status.  
• For the refund amount, use only the Federal refund amount, and not any total refund amount that includes a state refund.
• If you chose to pay TurboTax fees out of your Federal refund, then be sure to use the Federal refund amount before any fees were taken out.
• The amount to use is on your Federal Form 1040, Line 35a.
• You can also try phoning the IRS refund hotline.  I've seen it work for some users when the WMR tool didn't.  800-829-1954

If the IRS WMR tools says your refund is "still being processed", and if it's been longer than 21 days, we can tell you how you can try to phone the IRS to see if you can learn anything about the delay.

FAQ:  How do I track my state refund?

https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571

[xmasbaby0]

What email?  The IRS does not email you.   When you e-file your tax you will receive two emails from TurboTax.  The first one will say that your return was submitted.  The second email will tell you if your federal return was accepted or rejected.  If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.

Once your federal return has been accepted by the IRS, only the IRS has any control.  TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 35a of your 2021 Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others

If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.

https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

https://ttlc.intuit.com/questions/2724106-my-return-is-accepted-but-still-not-approved-is-there-a-pr...

[NCperson]

"accepted" simply means the IRS acknowledges receipt.  It does not mean that have reviwed, processed or approved the return.