It’s a busy time for filing lawsuits over the destruction of the world.

In 2018, seven cities, counties, and states filed lawsuits against the major oil and gas corporations, seeking to recover damages from climate-change-related disasters—bringing the total number of such lawsuits up to more than a dozen. Right before Thanksgiving, a group of West Coast crab fishermen sued 30 fossil fuel energy firms, alleging that global warming has led to fishery closures that resulted in tens of millions of dollars in lost revenue. In October, the New York attorney general, Barbara Underwood, filed a lawsuit against ExxonMobil claiming that the company misled its investors about potential liabilities connected to greenhouse gas emissions. The Massachusetts attorney general’s office is continuing a parallel investigation into whether ExxonMobil’s public statements about climate science misled consumers. And the landmark Our Children’s Trust lawsuit—in which 21 young people are suing the the U.S. government for fueling global warming—is still weaving its way through the court system after the Supreme Court decided not to hear the case.

Perhaps the most important climate liability case underway is taking place far from the American public’s eye. The plaintiff is a mountain guide named Saul Luciano Lluiya, who lives in the Peruvian city of Huaraz. In 2015, Luciano Lluiya sued the German utility RWE—the biggest power company in Germany—on the grounds that rising global temperatures, spurred in part by RWE’s coal burning, are accelerating glacier melt in the Andes and threatening deadly floods.

Last year, a Higher Regional Court in Germany (the equivalent of a U.S. Court of Appeals) ruled that the case could go forward. If Luciano Lluiya and his lawyers prevail, it would set an incredible legal precedent, one that would potentially allow carbon polluters to be held responsible for the impacts of climate change regardless of where those impacts are occurring.

Even the fact that Luciano’s case is able to go forward is a breakthrough. “Here you have one of the most conservative judicial systems in Europe, looking at whether a Peruvian farmer can sue a German company in Germany for harms that happened halfway around the world, and the judge says, ‘This is completely proper,’” says Carroll Muffett, president of the Center for International Environmental Law. “What it demonstrates is that there are cases like Luciano’s around the world. . . . And if more cases begin to emerge, then the future for the fossil fuel companies is dire.”

The RWE case is just one of many climate liability cases worldwide. One of the most closely watched efforts isn’t taking place in a court of law at all. In 2015, the Philippines Human Rights Commission initiated an investigation into whether a group of international fossil companies should be held accountable for the death and destruction caused by Typhoon Haiyan, the 2013 superstorm that battered Southeast Asia and led to some 6,300 deaths in the Philippines alone. During hearings in the Philippines, New York City, and London, the tribunal has heard testimony from Filipinos whose lives were torn apart by the storm and from climate scientists and other researchers.

The 47 fossil fuel companies being investigated by the human rights commission—which include Chevron, ExxonMobil, and Royal Dutch Shell—have refused to cooperate with the hearings and have argued that the commission has no authority to investigate their operations since they are not based in the Philippines. Yet legal observers and environmental activists say that the proceedings are adding to the body of evidence linking corporate activities to damages caused by climate change.

“The Philippine case isn’t about compensation—it’s about preventing future harms,” says Kristin Casper, a U.S.-based attorney who is heading Greenpeace International’s multinational cases against major carbon polluters. “It’s about getting businesses to really assess climate change risks and to then communicate those risks. And if those risks are real, then they have to take action to prevent harm.”

Other cases are also pressing fossil fuel corporations to make a full accounting of the risks of their business models. In October, a UK-based corporate accountablity group called Client Earth filed a suit against a Polish utility, Enea, for moving ahead with construction on a €1.2 billion coal plant despite what the plaintiffs call an “indefensible” financial risk. Friends of the Earth-Netherlands has initiated a legal complaint against Royal Dutch Shell in an attempt to force the oil giant to change its business model. According to newly released internal company documents, Shell’s executives worried that it would be held liable for climate change damages. Shell is also facing pressure in the United Kingdom, where a member of its British pension fund is threatening legal action against the company for allegedly not taking into account the costs of climate change. The tiny Pacific island country of Vanuatu is reportedly considering filing the first nation-state lawsuit against the fossil fuel corporations. (If you’re starting to feel as if you need a scorecard to follow along with the various climate change lawsuits, there’s now a website for this: Climate Liability News.)

While those cases target corporate actors, environmental advocates worldwide are using strategies similar to those in the Our Children’s Trust case to try to force national governments to take action on climate change. In April, the Supreme Court of Justice of Colombia ruled in favor of 25 youth plaintiffs who had sued their government. The court concluded that Colombia is facing “imminent and serious damage” from climate change and deforestation, and ordered the presidency and its ministries to develop an “inter-generational pact for the life of the Colombian Amazon” to halt deforestation there.

Three years ago, A Dutch court ruled in favor of 886 Dutch citizens represented by the Urgenda Foundation who argued that their government’s slow response to climate change violated their rights as guaranteed by the European Convention on Human Rights. In October, the Hague Court of Appeals upheld the original ruling that the Dutch government must reduce greenhouse gas emissions by 25 percent from 1990 levels by 2020.

In late November, a Quebec-based environmental group called ENvironnement JEUnesse filed a class action lawsuit on behalf of all Quebec residents younger than 35. The lawsuit charged that the Canadian government’s efforts to reduce emissions were insufficient and violate young people’s rights as established by the Canadian Charter of Rights and Freedoms. Similar legal challenges against national governments have been filed in Belgium, Ireland, New Zealand, Norway, Pakistan, and Switzerland.

These far-flung cases are on the frontier of testing new legal theories. “The ability of the law to force the carbon majors to change their business models is a big, wide-open question, and the plaintiffs face significant obstacles,” says Michael Burger, director of the Sabin Center for Climate Change Law at Columbia Law School. Still, says Burger, he expects to see more and more types of litigation.

Some of the attorneys involved in these efforts have been surprised by the speed at which the legal challenges against the carbon polluters and national governments have piled up. That pace, they say, is due in part to the increasing urgency surrounding climate change as climate-related disasters become more destructive and deadly. The slew of lawsuits is also a result of the advances in what’s called “attribution science”—the ability of researchers to detail the precise share of any one company’s or country’s historic greenhouse gas emissions.

“If you look at these cases together, you see a growing diversity of legal claims: human rights suits from the impact of glacier melt, suits on behalf of consumers, on behalf of investors,” Moffett at the Center for International Environmental Law says. “That’s where the analogy to the Big Tobacco litigation [of the 1990s] is telling. It took decades to get to the place the climate liability cases have gotten to in just a few years. It took decades before a court acknowledged the wrongdoing of the tobacco producers. Now, people are going into court with the evidence [about climate change impacts] already in hand in their complaints. And that evidence is cross pollinating across these cases.”

Michael Burger agrees that such “cross pollination” is important. While U.S. courts are not bound by any precedents set in other countries’ legal systems, Burger says that American judges do pay attention to what happens abroad. “Judges who get these [climate change] cases and the clerks who work for them become aware of other cases in the U.S. and around the world,” he says. “So if a case comes out of Germany, then other judges may look to that to better understand the rationale and the reasoning. . . . There’s no question that judges are involved in some kind of dialogue with each other.”

Climate liability efforts—ambitious though they may be—are unlikely to single-handedly address the climate crisis. Yet there are signs that the lawsuits are already changing some of the political calculus underlying the behavior of fossil fuel companies. Some, like Shell, are starting to be much more forthright in disclosing climate liabilities to their investors. And during a landmark hearing in U.S. federal court in San Francisco last spring, all the major oil companies were forced to acknowledge the scientific consensus that the burning of fossil fuel is the primary driver of global warming—an admission that represents yet another nail in the coffin of climate science denial.

It’s too early to know when or where a major climate liability verdict will be issued against one of the fossil fuel corporations. It could happen in a U.S. court, a German one, a British one, or perhaps from some unlooked-for direction. But this much is clear: A judgment is coming.