The top United Nations court took up the largest case in its history on Monday, hearing the plight of several small island nations helpless in combating the devastating impact of climate change that they feel endangers their very survival. They demand that major polluting nations be held to account.

After years of lobbying by island nations who fear they could simply disappear under rising sea waters, the U.N. General Assembly asked the International Court of Justice last year for an opinion on “the obligations of States in respect of climate change.”

Europe’s highest human rights court threw out cases on Tuesday brought by six Portuguese youths and a French mayor aimed at forcing countries to meet international obligations to reduce greenhouse gas emissions, but sided with a group of senior Swiss women who also sought such measures.