From the Supreme Court's opinion in District of Columbia v Heller, written by Scalia, arguably the most conservative justice on the Court:
2. Like most rights, the Second Amendment right is not unlimited.
It is not a right to keep and carry any weapon whatsoever in any
manner whatsoever and for whatever purpose: For example, concealed
weapons prohibitions have been upheld under the Amendment
or state analogues. The Court’s opinion should not be taken to cast
doubt on longstanding prohibitions on the possession of firearms by
felons and the mentally ill, or laws forbidding the carrying of firearms
in sensitive places such as schools and government buildings, or
laws imposing conditions and qualifications on the commercial sale of
arms. Miller’s holding that the sorts of weapons protected are those
“in common use at the time” finds support in the historical tradition
of prohibiting the carrying of dangerous and unusual weapons.