A growing number of court cases are being brought against governments, administrations, and corporations in support of enhanced climate action. This is the first of two articles that examine climate litigation as a social process and potential driver of deep decarbonisation from a perspective that combines legal, social, and political science. Contributing to an emerging interdisciplinary research agenda on the dynamics and effects of climate litigation and on its societal embeddedness, we present and test two analytical tools, the Social Plausibility Assessment Framework and the Global Opportunity Structure for Climate Action. The first article introduces these analytical tools, and applies them to assess the overall evolution of climate litigation and identify developments in its legal and societal context that enable or constrain future driver dynamics. Based on this assessment, we conclude that climate litigation constitutes an important but on its own insufficient driver of deep decarbonisation, which is shaped by, and continuously shapes, legal, socio-political, economic, and scientific scripts and repertoires that enable novel forms of societal agency. The second article further operationalises and illustrates the approach by zooming in on a case-specific level and examining two recent landmark decisions in the Netherlands and Germany.