Usually interstate suits involve issues like interstate water compacts (such as the case of Montana v. Wyoming and North Dakota decided the same day).
The U.S. Supreme Court today denied them relief by a 6-2 vote without an opinion other than from the two dissenting judges (Justice Thomas writing for himself and Justice Alito). The dissent was on grounds of constitutional procedure and is illuminative of how the original jurisdiction of the U.S. Supreme Court works:
Federal law does not, on its face, give this Court discretion to decline to decide cases within its original jurisdiction. Yet the Court has long exercised such discretion, and does so again today in denying, without explanation, Nebraska and Oklahoma’s motion for leave to file a complaint against Colorado. I would not dispose of the complaint so hastily. Because our discretionary approach to exercising our original jurisdiction is questionable, and because the plaintiff States have made a reasonable case that this dispute falls within our original and exclusive jurisdiction, I would grant the plaintiff States leave to file their complaint.While I agree with the results on the merits, Justice Thomas makes a respectable point on the process used to arrive at this conclusion.