Per the ATF:
To qualify for importation under 18 U.S.C. § 925(d)(3), a firearm or ammunition must not fall under the definition of firearm as defined in 26 U.S.C. § 5845(b), and must be of a type generally recognized as particularly suitable for or readily adaptable to sporting purposes.
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Note: ATF has determined that certain features designed for military application are indicative of non-sporting rifles and shotguns. Features which are not recognized as sporting include, but are not limited to, folding or telescoping stocks, pistol grips that protrude conspicuously beneath the action of the weapon, a bayonet or bayonet mount, a flash suppressor or threaded barrel designed to accommodate a flash suppressor, a grenade launcher and night sights.
Long story short, the only firearms it's generally permissible to import are hunting-type rifles - there is a practice amongst gun culture of replacing enough parts of foreign MSSAs/banned firearms with US-made parts to comply with the law, but while distasteful, it's not really a large enough area to warrant much concern.
Further information is available at the linked ATF page; the "Report and Recommendation of the ATF Working Group on the Importability of Certain Semiautomatic Rifles" is particularly good in outlining just how hard it is to import MSSAs.
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