It depends -

If your wife was here on an H-4 visa during 2017, she may be considered a US resident alien for all of 2017 if she meets the substantial presence test during the time she was here on this H-4 visa. In this instance, she would be required to file a US income tax return if her income is above the income threshold for filing.

For F-1 visa holders, she will be exempt from the Substantial Presence Test for the first 2 (if non-student) or 5 (if student) calendar years that she is in the US. This means that she would be considered a non-resident aliens for US tax purposes under the F-1 visa.

See this link for additional information US Tax Guide for Aliens.

For your US tax filings, you will either have to file a married filing separately or married filings jointly.

You can file jointly with your nonresident alien spouse but if your spouse does not have a Social Security Number (SSN) or Individual Taxpayer Identification Number (ITIN), you will need to apply for one. To apply for an ITIN, you would use Form W-7 and would need to attached your tax return to this form (see below).

Click here for more information about Claiming Non-Citizen Spouse and Children On Your Taxes.

You have 3 main options for filing your income tax return:

• Option 1 - Married Filing Jointly and you claim an exemption for your spouse. Your spouse will be treated as a US resident alien for US tax purposes and all of your spouse's worldwide income in USD will be subject to being taxable as a US citizen or resident alien.

Here are some additional steps for filing married filing jointly if spouse needs an ITIN. 

• leave NRA spouse's SSN blank and print a paper copy of your tax return.
• skip error check section if only error is missing SSN for spouse.
• under the file tab, you will need to select "file by mail" and print a copy of your federal income tax return.
• attach a statement, signed by both spouses, to your joint return for the first tax year for which the choice applies (Nonresident Spouse Treated as a Resident). It should contain the following information:
•  A declaration that one spouse was a non-resident alien and the other spouse a U.S. citizen or resident alien on the last day of your tax year, and that you choose to be treated as U.S. residents for the entire tax year.
• The name, address, and identification number of each spouse.
• apply for NRA spouse’s Individual Taxpayer Identification Number (ITIN) using Form W-7 (Click ITIN). (You will need to apply for a ITIN if filing married filing separately and taking an exemption for NRA spouse and that NRA spouse does not have a SSN. (see option 3 below))
• attach a copy of your Form W-7 (along with the necessary supporting documents) to your tax return (For the supporting documents, one option is for your NRA spouse to get a certified copy of his/her passport which will need to be included with your tax return filing.) Click here for IRS website  ITIN - Frequently Asked Questions .
• mail your tax return along with your declaration statement, Form W-7 and supporting documents to the IRS. According to the IRS, because you are filing your tax return as an attachment to your (ITIN) application, you should not mail your return to the address listed in the Form 1040, 1040A or 1040EZ instructions. Instead, send your return, Form W-7 and proof of identity and foreign status documents to:
  
       Internal Revenue Service
       Austin Service Center
       ITIN Operation
       P.O. Box 149342
       Austin, TX 78714-9342 
  
  You may also apply for an ITIN using the services of an IRS-authorized Acceptance Agent or visit some key IRS Taxpayer Assistance Center in lieu of mailing your information to the IRS in Austin.
• State filing - You will want to file an extension for your state until you receive your ITIN. This is because the application for your ITIN is a federal filing. Most state will not process your return without either a SSN or an ITIN. (However some states will accept state filings with W-7 attachments. Please contact your state for more information using the State Department of Revenue Contacts and ask if your state will accept a state tax return with a Form W-7 attached).  
  When the IRS assigns you an ITIN, update your returns (both federal and state) in TurboTax with this new information and then you should be able to e-file your state return.
  Because many states give an automatic extension when you file the federal extension Form 4868, just file a federal extension even if you don't think you will need it for your federal tax return.  But check with your state's Department of Revenue to make sure that your state doesn't have a separate state extension filing.

• Option 2 - Married Filing Separately (includes head of household (HoH), if you have a "qualified relative"- see US citizens and Resident Aliens Abroad - Head of Household) and you are NOT taking an exemption for your NRA spouse.
• leave spouse's SSN blank.     
• hand-write "NRA" in all of the places on your tax return that require your NRA spouse's SSN (IRS - Married Filing Separately).
• skip the error check section as long as your only error is missing spouse's SSN.
• mail in your return (you will not be able to efile your tax return so choose "file by mail" in TurboTax).
• mail to IRS address printed with your return.
• Option 3 - Married Filing Separately (or HoH) and you claim an exemption for your NRA spouse (You can claim an exemption for your spouse only if your spouse had no US source income, isn't filing a US tax return, and isn't the dependent of another person other than yourself).
• leave NRA spouse's SSN blank (if no SSN or ITIN). 
• Under the Personal Information section, choose the box for "NRA spouse" option and select all the questions on the next screen regarding your NRA spouse.
• skip the error check section as long as your only error is missing spouse's SSN.
• If your NRA spouse does not have a SSN or ITIN, under the file tab, you will need to select "file by mail" and print a copy of your federal income tax return.
• apply for NRA spouse’s Individual Taxpayer Identification Number (ITIN) using Form W-7 (Click ITIN)(see above for information about filing a Form W-7 with your tax return.)
• mail in your return with Form W-7 to the IRS address listed above.