Prior to 1934, everything was completely legal, no registration or anything. The National Firearms Act of 1934 created Title I and Title II firearms. Title I consists of Rifles, Shotguns, Handguns, and Firearms. These are not registered, but must be transferred over state lines by a dealer. Title II consists of Weapons Made From a Rifle (typically an SBR), Weapons Made From a Shotgun (Typically an SBS), Silencers, Destructive Devices, Any Other Weapons, and Machine Guns. Title II must be registered with the ATF at the time of manufacture and transfer.
In 1968, the Gun Control Act banned the importation of Title II firearms.
In 1986, the Firearm Owners Protection Act had a poison pill added to it in an attempt to prevent it from passing. That poison pill banned the registration of Machine Guns, but not the transfer.
So, prior to 1934, anyone could own whatever they wanted. After 1934, anyone could still own whatever they wanted as long as they paid the ATF $200 for their Title II firearms.
After 1968, foreign Title II weapons were no longer allowed to be imported. You could however import a Title I foreign firearm and convert it to Title II once it was in the US.
After 1986, Machine Guns could no longer be registered. Prior to that, anyone could make one. You could either buy one that came that way from the factory as long as its transfer to you was registered with the ATF, or you could buy a Title I firearm and convert it to Title II after registering it with the ATF. You can still do that with all Title II firearms, except Machine Guns.