Cases against governments
Over the last ten years, cases have been heard in courts all over the world. The first to succeed was brought by the Dutch environmental group Urgenda -- see the link below. Urgenda also runs the Climate Litigation Network, which supports organisations, communities and individuals pursuing litigation aimed at compelling national governments to up their climate mitigation ambition. The CLN website lists 26 cases in 22 countries. The international organisation Client Earth, together with the UK Good Law Project, has recently won an important case in the UK's High Court -- also linked to below.
The Good Law Project and Client Earth win court case to oblige UK Government to fulfil its climate commitments
The Labour Government's Climate Change Act of 2008 set a sequence of six legally binding "carbon budgets", with the last now containing a commitment to reach net zero by 2050. "Legally binding" means that courts are empowered to assess government action, and can order the government to strengthen it to achieve the statutory targets. In July 2022 the Good Law Project and Client Earth won a High Court judgement that "the proposals for achieving Net Zero approved by the Secretary of State were too vague to enable [the judge] to be satisfied that the statutory targets would be met." The court ordered that the existing Strategy be fleshed out with the detail necessary for Parliamentary – and public – scrutiny within the next 8 months. The Government was ordered to pay Good Law's legal costs.
Urgenda wins case to oblige Dutch government to reduce emissions
On 20 December 2019, the Dutch Supreme Court, the highest court in the Netherlands, upheld the previous decisions in the Urgenda Climate Case, finding that the Dutch government has obligations to urgently and significantly reduce emissions in line with its human rights obligations. This was the first case in the world in which citizens established that their government has a legal duty to prevent dangerous climate change. On 24 June 2015, the District Court of The Hague had ruled that the government must cut its greenhouse gas emissions by at least 25% by the end of 2020 (compared to 1990 levels). The District Court’s decision was appealed by the State and upheld by the Court of Appeal on 9 October 2018. The State then appealed to the Supreme Court, which ruled in favour of Urgenda on 20 December 2019.

Cases against governments
Could these cases be one of the reasons why the UK Government wants to withdraw from the European Court of Human Rights?