With a Form 4, you mail the paperwork to an ATF office in Atlanta. They take your paperwork, remove the check/MO and deposit it. Your forms are then sent to the ATF office in West Virginia for processing. Once the form arrives in WV and is processed, it gets assigned to an inspector's queue. Once it is assigned to a queue, it is in 'pending' status. That said, if you call the ATF and ask what inspector has your paperwork they may give you the wrong name. I was told my SDN-6 was bring handled by Al Lamberger, but it was signed off by Brittany Brown.
You can check the status of your forms, and get your pending date, by calling the ATF in West Virginia - 304-616-4500. You will need to give them your serial number, the name of the dealer you bought it from, and your name.
The main cause of the extended wait is simple backlog. Before some of the changes made a few weeks ago to help speed things up, the ATF was something like 80,000 forms behind. They received 199,900 forms last year for processing.
The current wait times from PENDING to APPROVED is running around 7 months. From the time your paperwork gets to Atlanta to the time it is PENDING is usually 4-8 weeks. Both of my Form 4s that have come back in the last 2 months were approved almost exactly 9 months after being received in Atlanta.