This contribution takes the form of an uncommon case report. It discusses an action brought to the Court of Justice of the European Union (CJEU) before the final decision has been rendered. The author believes this is justified because the innovative character of the procedural and substantive reasoning of the application could be of interest to a wider public. This may be the case even if the CJEU eventually dismisses the action as being inadmissible, leaving the substantive questions undecided. The applicants in Carvalho and Others v. European Union claim that European Union (EU) law does not limit greenhouse gas (GHG) emissions as strictly as is required by EU human rights and international law. The case note explains the parties in the case, the acts being challenged, the relief being sought, and the content and application of the relevant procedural and substantive law. The case is illustrative of the high barriers for direct access to the CJEU, and suggests how they might be overcome. It is also a laboratory for examining the interface of climate science, economics, and law. At this interface, available emissions budgets and the technical and economic feasibility of emissions reductions are calculated and made legally relevant. Carvalho is based on the applicants’ conviction that, where the EU assumes a regulatory competence such as that of GHG emissions reduction, it must exercise it in accordance with its human rights and international obligations.