https://turbotax.intuit.com/tax-tools/efile-status-lookup/

TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.

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 20 of your 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

On the IRS site you are also offered the use of an app called IRS2Go

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...

Only the taxpayer or their representative can legally inquire about the status of a tax return or a tax refund.

Any tax preparation service can estimate the date you will receive a tax refund based on the IRS target of issuing the federal tax refund within 21 days after the federal tax return was accepted.  No one can give you a date certain since Only the IRS and your State control when and if a Federal or State tax refund is Approved and Issued.

To check the status of an e-filed return, open up your desktop product or log into your TurboTax Online Account. You can find your status within the TurboTax product.
If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds
If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
If over 21 days since being Accepted by the IRS and the tax refund is still Processing you can call the IRS and speak with an IRS agent concerning your tax refund.
Call the IRS: 1-800-829-1040 hours 7 AM - 7 PM local time Monday-Friday
When calling the IRS do NOT choose the first option re: "Refund", or it will send you to an automated phone line.
So after first choosing your language, then do NOT choose Option 1 (refund info). Choose option 2 for "personal income tax" instead.
Then press 1 for "form, tax history, or payment".
Then press 3 "for all other questions."
Then press 2 "for all other questions."
- When it asks you to enter your SSN or EIN to access your account information, don't enter anything.
- After it asks twice, you will get another menu.
Then press 2 for personal or individual tax questions.
It should then transfer you to an agent.