This chapter explores “trust-rights” climate litigation, claiming sovereign obligations to protect the atmosphere, public rights to climate stability, or both. It begins with scholarly consideration of these strategies, reviewing sources of environmental rights, application of public trust principles to climate, and critiques of the atmospheric trust. It reveals the hidden duality of trust-rights climate claims as a pairing of reciprocal rights and duties. Then it reviews the explosion of trust-rights climate advocacy around the world, including the conclusion in Urgenda Foundation v. Netherlands that the nation had failed its duty under the European Convention on Human Rights to limit contributions to climate change; the failed attempt in Juliana v. United States to partner an atmospheric trust claim with constitutional rights asserted under the Due Process Clause; and a new generation of advocacy to build trust-rights principles into U.S. state constitutions. Finally, it considers the arguments against – and in favor of – trust-rights advocacy, addressing both constitutional concerns about the separation of powers and practical concerns about bringing uncertain impact litigation.