SCOTUSBlog has as good a summary of the two cases as can be found anywhere:
In both cases, the issue is whether the human rights laws at issue apply to someone other than a natural person — corporations in Kiobel, political or other organizations in Mohamad. In both cases, federal appeals courts found that non-natural persons are immune from liability, differing with other appeals courts’ rulings. The Kiobel decision came from the Second Circuit Court, the Mohamad ruling from the D.C. Circuit Court.
Bexis at Drug and Device Law makes his opinion clear:
The Alien Torts Claims Act has a laudable purpose, but like all too many things in our legal system, that purpose has been systematically distorted in recent years by plaintiffs looking for ever more ways to expand liability to ever more ridiculous lengths. While this jurisdictional basis was not exactly the relief we were looking for when we criticized Abdullahi, we’ll take what we can get – if we can get it.
Jeremy D. Frey and Frank C. Razzano of Pepper Hamilton want SCOTUS to lay down some limits:
For most, the Supreme Court’s grant of certiorari in Kiobel and Rajoub cannot have come soon enough.
The need to cabin the ATS finds support in the first Congress’s original purpose to avoid disruptions in our foreign relations. Interpreting the ATS to assert universal jurisdiction of the federal courts over international law torts — limited only by due process for defendants — invites foreign nations and their courts to return the favor. This is not just bad policy. It promotes disorder among the community of nations. Hopefully, the Court will seize the opportunity to bring much-needed clarity and impose additional limiting principles on the reach and jurisdiction of the ATS and the TVPA.