This just happened to me, so I feel particularly qualified to provide an answer. Bear in mind that I live in Florida, and the process might vary state to state.When you fill out an ATF form 4473 to get approval for a firearm purchase/transfer, you can receive one of a few different responses:Approved, not approved, or delayed.If approved, you’re good to go.If delayed, you get to play the short waiting game. You’ll see why I said short in a moment, but the only option you have is to wait and call the FFL through which you are purchasing the gun once a day to check the system for an update.After 3 days business days of being delayed without a decision, the FFL can legally complete the transfer to you if they so choose, but they aren’t required to do so, and many won’t.If the delay ends up returning an approval, you’re good to go.Then there’s what just happened to me. I called the FFL, told them I was delayed and just checking to see if I’d been approved, and the guy checked and said No, you weren’t delayed, you were denied.I’ve never been delayed before, so by this point I had already researched the potential outcomes and what would happen if, for whatever reason I was not approved, but it was still a gut punch to hear those words.Here comes the long wait I mentioned earlier.First, you have to go to the FFL where you applied for the transfer and ask for an appeal form. They will fill it out and give it to you.Next, take that to your local sheriff/jail to get fingerprinted. Wait to fill out the buyer’s portion of the form until you get fingerprinted - the lady who fingerprinted me said I needed to sign it in front of her.Send the complete appeal form with your fingerprints to the state department listed in the instructions on the form. Since I live in Florida, I had to send mine to the Florida Department of Law Enforcement (FDLE).You have 60 days from the date of the non-approval to appeal the decision.Surprisingly, my appeal decision letter came back within a couple weeks, but I’ve heard it can take much longer.Bring that letter to the FFL and pick up your gun(s).Again, that is the process in my state. I hope you don’t have to go through it, but if you do get a non-approval and you know you are eligible to purchase/possess firearms where you live, ask the FFL how to appeal it and they’ll tell you how.