Depending on how the court rules, it could also affect a narrow legal path that helped families of the mass shooting at Sandy Hook Elementary School secure a $73 million settlement from the gun maker Remington.
The arguments are coincidently unfolding the day President Donald Trump's long-threatened tariffs against Mexico and Canada went into effect, putting global markets on edge and setting up costly retaliations.
Here's what to know about the case:
Why did Mexico sue U.S. gun companies?
Mexico has strict gun laws and has just one store where people can legally buy firearms. But thousands of guns are smuggled in by the country's powerful drug cartels.
The Mexican government says 70% of those weapons come from the United States. The lawsuit claims that companies knew weapons were being sold to traffickers who smuggled them into Mexico and decided to cash in on that market.
The defendants include big-name manufacturers such as Smith & Wesson, Beretta, Colt and Glock. The lawsuit is still in its early stages, and if the court does side with Mexico it would still have to prove the allegations.
What do the gun companies say?
The gun makers say there is no evidence the industry allows trafficking and they disagree with Mexico's data about how many weapons originate in the U.S. The Mexican government, not U.S. gun makers, is responsible for enforcing the laws and fighting crime, they argue.
The industry is shielded from most civil lawsuits arising from crimes committed using firearms under a 20-year-old law, though Mexico has argued that it doesn't apply to crimes committed outside of the U.S.
The gun companies are asking the justices to overturn an appeals court ruling that allowed the case to move forward.
The 1st U.S. Circuit Court of Appeals found it fell under an exception to the shield law for situations in which firearm companies are accused of knowingly violating the law.
What happens next?
That exception has come up in other cases.
The victims of the 2012 mass shooting at Sandy Hook argued it applied to their lawsuit because the gun maker had violated state law in the marketing of the AR-15 rifle used on the shooting, in which 20 first graders and six educators were killed.
The Supreme Court declined to hear that case. After reaching the $73 million settlement, the families said they hoped it would lead to more safety and accountability.
Depending on how the justices rules, their eventual findings could narrow or close that legal path.
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