The 1968 Gun control Act, the 1934 National Firearm Act.
Until May 1968, you could buy a FA at Sears... then post 68, you just had to register it by May 1986.
As long as you have a clean background and pay 200 bucks to the ATF, you can still buy an FA... just need some $$$$ to buy the actual weapon. Cheapest entry in it will be a Mac-10, at nearly $8,000