Climate lawsuits have reached the courts. While the initial rulings primarily address the obligations of states and major CO2 emitters, future cases will require courts to consider issues of compensation. This volume aims to shed light on the following questions: How can compensation for climate loss and damage be claimed? At what point can CO2 emissions be considered harmful? How do the courts engage with climate science? How is climate damage quantified? How should historical CO2 emissions be assessed to determine a just amount of compensation in an intergenerational and transnational context? Bringing together legal experts from private and public law as well as experts from the insurance industry, the social sciences, and economics, this volume is essential reading for anyone concerned with climate damage.