Link to the recent federal court ruling that the Second Amendment covers a right to carry guns in public:
This is a trial-level court. The case still has to work its way through the appeals process.
The court ruled that "intermediate scrutiny" was the proper standard for considering laws on carry permits.
The court ruled that "may issue" carry permits (where people can only get a license if they demonstrate that they "have a need" to carry a gun) do not pass muster with intermediate scrutiny. Instead a license can only be denied if the government can show a good reason why that particular person should not be allowed to carry a gun.
The court did not rule whether there was any right to carry concealed vs open (though clearly at least one of the two would have to be allowed).