Hello, and thank you for writing. I guess the answer to your question depends on what the lender means by "underwriting." Here's how it usually goes:
See How long does it take to close on a house? for more information https://themortgagereports.com/19487/how-long-does-it-take-to-close-a-mortgage-gina-pogol
You provide your lender with information required to complete the Fannie Mae Form 1003 -- your identifying information, employment, income, down payment source, and assets like bank accounts and investment / retirement accounts.
Your lender inputs this information into an automated underwriting system, or AUS. The system checks your credit, analyzes your information and issues a recommendation -- approve, refer (which means it needs more information) or refer with caution (which usually means a decline). If you get approved, the AUS also generates a list of documents required to verify that the information you provided is true -- for instance, pay stubs and bank statements.
This may also be referred to as "processing." https://themortgagereports.com/37333/my-mortgage-is-in-processing-what-does-a-mortgage-loan-processor-do
A human underwriter looks at those documents, makes sure that they support the income and assets listed, and then you get your pre-approval or credit approval letter. Or you might get a request for additional information, but you should never just be left hanging. A pre-approval means that as long as the property meets the lender's guidelines, you should be able to close.
If you have a property under contract, the lender orders an appraisal to make sure that the property is worth the purchase price, and that there are no problems with its livability, health, safety or marketability, should they need to foreclose. Once the appraisal comes in and the lender approves it, you have full or final approval and should be clear to close.
So your file could be "in underwriting" and also at any one of these stages. You may have nothing to worry about. The chief issue I see here is that there appears to have been insufficient communication between you and your lender. Call and ask what the status is on your application. Ask for a pre-approval letter. Ask if anyone has ordered an appraisal. Ask when you can expect to close. And if you don't like the answers you get, find another lender.