Five years ago, the United Nations Paris climate agreement set a ceiling for global warming at well below 2 °C, ideally 1.5 °C relative to pre-industrial levels. World leaders also agreed to balance greenhouse-gas emissions in the second half of the century, so that the sum of all greenhouse gases emitted from human activities is zero. In response, ever more countries, institutions and companies are announcing net-zero targets1,2. Recent examples include the United States, China, the European Union, the technology firm Microsoft and an alliance of European airports. These welcome signs of intent come with difficulties.