From the slip opinion at 54-55:
[N]othing in our opinion should 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. [fn: We identify these presumptively lawful regulatory measures only as examples; our list does not purport to be exhaustive.]
We also recognize another important limitation on the right to keep and carry arms. Miller said, as we have explained, that the sorts of weapons protected were those “in common use at the time.” 307 U. S., at 179. We think that limitation is fairly supported by the historical tradition of prohibiting the carrying of “dangerous and unusual weapons.” [citations omitted]
Relatedly, here’s the analysis of why the handgun ban violates the individual Second Amendment right on 56-58:
[T]he inherent right of self-defense has been central to the Second Amendment right. The handgun ban amounts to a prohibition of an entire class of “arms” that is overwhelmingly chosen by American society for that lawful purpose. The prohibition extends, moreover, to the home, where the need for defense of self, family, and property is most acute. Under any of the standards of scrutiny that we have applied to enumerated constitutional rights, banning from the home “the most preferred firearm in the nation to ‘keep’ and use for protection of one’s home and family,” 478 F. 3d, at 400, would fail constitutional muster.
. . .
It is no answer to say, as petitioners do, that it is permissible to ban the possession of handguns so long as the possession of other firearms (i.e., long guns) is allowed. It is enough to note, as we have observed, that the American people have considered the handgun to be the quintessential self-defense weapon. There are many reasons that a citizen may prefer a handgun for home defense: It is easier to store in a location that is readily accessible in an emergency; it cannot easily be redirected or wrestled away by an attacker; it is easier to use for those without the upper-body strength to lift and aim a long gun; it can be pointed at a burglar with one hand while the other hand dials the police. Whatever the reason, handguns are the most popular weapon chosen by Americans for self-defense in the home, and a complete prohibition of their use is invalid.
Of course, the DC government may now try again, enacting another gun restriction that is less severe; presumably that law will need to be litigated, as well, which will force the courts to tell us more about the degrees of scrutiny.