"At issue is whether corporations and political groups can be held liable in U.S. courts for their roles in torture and other abuses abroad."And there is another issue that may even be more important. This has to do with the Citizen's United decision essentially - many argue - giving personhood to corporations. See the Guardian UK for more on corporate liability.
The issue is "whether US-based and global corporations can be held liable for genocide and other violations of international law."There are two cases to be decided by the US Supreme Court. "[T]he case of a dozen Nigerians who sued the Royal Dutch Shell oil company in the torture and execution of dissidents in Nigeria in the 1990s." And "a lawsuit against the Palestinian Authority and the Palestinian Liberation Organization" where a Palestinian American "was allegedly tortured and killed by Palestinian intelligence officials in the 1990s." [Los Angeles Times].
But go back to the KGW story for more details about what is at stake with these and similar cases. "Other cases pending in U.S. courts seek to hold accountable Chiquita Brands International for its relationship with paramilitary groups in Colombia; Exxon and Chevron for abuses in Indonesia and Nigeria, respectively; Britain-based mining concern Rio Tinto for allegedly aiding the Papua New Guinea government in a civil war; and several companies for their role in the old racial apartheid system in South Africa." [Justices weigh foreigners' suits vs. companies]
See Harvard's International Human Rights Clinic on how this law has been used "to hold perpetrators to account for violations such as extrajudicial killing, torture, war crimes, and crimes against humanity." See Wikipedia for a brief description of the Torture Victims Protection Act and its use. And, see this law review article from Boalt Law School, Berkeley Journal of International Law, Vol, 28:2, that explains the connection between the two statutes plus providing their legislative histories and court interpretations.