In 2009, the EPA concluded that greenhouse gases were, in fact, bad, and that unchecked increases were a threat to the health of current and future generations. So it then levied regulations on emissions from both vehicles and fixed sources, like powerplants and factories. According to the NYT, this has not sat well with certain groups, which are claiming that the EPA hasn't provided enough evidence to support its claims against stationary sources.
The Supreme Court accepted six petitions, although the only issue it's going to consider is whether the EPA "permissibly determined that its regulation of greenhouse gas emissions from new motor vehicles triggered permitting requirements under the Clean Air Act for stationary sources that emit greenhouse gases." What that means in simple English is that SCOTUS isn't ruling on the legality of the EPA regulating tailpipe emissions, but that it's considering whether or not the agency had the right to extend those regulations to so-called fixed sources, like power plants.
For more legalese, the NYT spoke to Richard J. Lazarus, an environmental law professor at Harvard, who said, "The court declined to review EPA's determination that greenhouse gases from new motor vehicles endanger public health and welfare and therefore has left intact the government's current regulation of motor vehicle emissions to address climate change." Translated, EPA vehicle emissions regulations are as legal as can be, and no matter the results of this case, that isn't going to change.