NEW YORK (REUTERS) - A landmark ruling on Wednesday (May 26) by a Dutch court ordering Royal Dutch Shell to drastically cut its planned greenhouse gas emissions could impact the United States, where most of the world's climate cases are being litigated.

About 1,375 lawsuits seeking relief from climate change have been filed in US courts, compared with about 425 in other various countries, according to the Sabin Centre for Climate Change Law at Columbia Law School.

The following is a summary of how litigation of the most significant cases is playing out across the US:

About two dozen lawsuits have been filed by local governments and states, which have accused major oil and gas companies of contributing to the effects of global warming by selling fossil fuels whose burning generates greenhouse gases.

States that have sued these companies include Rhode Island, Delaware and Connecticut.

The lawsuits, which are pending, target companies including BP, ExxonMobil and Chevron. The businesses deny the allegations and say that the suits do nothing to address the challenge of climate change.

The plaintiffs are seeking monetary damages to pay for seawalls and other infrastructure to guard against extreme weather and rising sea levels brought on by climate change.

In April, New York City lost a lawsuit in a federal appeals court. It sought to hold five major oil companies liable for global warming. The judge said the risk of "stepping on the toes of the political branches" barred the city's suit, among other reasons.

A handful of lawsuits, including by the District of Columbia and the state of Minnesota, allege that oil and gas companies have misled the public by knowingly downplaying the threat of climate change.

In one securities lawsuit, investors said ExxonMobil Corp and its executives failed to properly account for the impact of climate on its business and made public statements and financial disclosures that caused its share price to fall. ExxonMobil has said the allegations have no merit.

Some lawsuits by environmentalists also accuse oil and gas companies of failing to adequately protect coastal fuel terminals in Rhode Island and in Massachusetts against the risks of flooding caused by sea level rise.

Meanwhile, a group of young Americans suing the federal government over actions they say contribute to climate change are in settlement talks with the Biden administration.