The fight over who should pay the soaring costs of climate change — the intensifying wildfires, storms and heat waves — has moved to the courts.

Nationwide, more than 60 state and local governments have filed dozens of lawsuits seeking damages from oil companies over global warming, which is caused by the burning of fossil fuels. With a president who has called climate change a hoax and a gridlocked Congress, courtrooms have become one of the few remaining options for communities seeking relief.

“Globally, neither national legislatures nor governments are taking adequate action, and so the advocates of climate action are turning to the courts,” said Michael Gerrard, director of the Sabin Center for Climate Change Law at Columbia University.

Now the highest court in the land has entered the fray. On Monday, it heard arguments over a lawsuit filed by the city and county of Boulder, Colo., against two energy companies. Many, if not most, of the dozens of other cases nationwide hinge on the Supreme Court’s decision.

The city and county had sued Exxon Mobil and Suncor Energy, claiming they misled the public about climate change and should pay for damages. The energy companies have asked the Supreme Court to throw out the case.

One of the industry’s main arguments has been that climate change is too complex a problem to be handled by individual courts. “This case and others like it reflect an all too regrettable trend of trying to resolve major political issues in court rather than leaving them to the political branches where they belong,” Kannon Shanmugam, a lawyer for the companies, told the justices on Monday.