The idea of getting the court to issue a legal opinion was originally proposed by Fiji law students five years ago.
It was then followed by Vanuatu, an island nation with bitter experience of the effects of rising temperatures and sea levels.
Last year, about 80% of the population was affected by a double cyclone.
The extent of the damage forced the government to declare a six-month state of emergency.
Under pressure from Vanuatu and many other countries, the UN General Assembly referred two important climate issues to international judges at the ICJ.
They relate to the obligations of countries under international law to protect the Earth’s climate system from polluting emissions of greenhouse gases.
But they also asked the court to rule on the legal consequences of those obligations in cases where states “through their actions and inactions have caused significant damage to the climate system and other parts of the environment.”
Vanuatu will be the first country to give evidence at today’s hearing in the Netherlands.
“We are on the front lines of the impacts of climate change,” Ralf Regenvanu, Vanuatu’s special envoy, told reporters before the hearing.
“Our call for an advisory opinion from the International Court of Justice on Climate Change comes at a pivotal moment… a moment that clearly establishes international legal obligations for climate action.”
Although the court’s decision is not binding, the outcome could be used in other court cases where small island states seek financial compensation from developed countries for losses and damages they have suffered as a result of historical emissions of global warming gases the planet .
The trial took place just a week after the end of the COP29 climate summit in Azerbaijan.
A decision by the richer world to commit $300 billion annually in climate finance until 2035 has sparked anger among developing countries, which have argued that it is not enough for their needs.
In The Hague, the court will also hear a number of countries, including the United States and China, as well as representatives of the oil-producing group OPEC.
The hearings will last until December 13, and the verdict is expected in 2025.