In the past year, consumer giant Johnson & Johnson has been hit with four jury verdicts totaling about $300 million in cases linking its popular baby powder to ovarian cancer. With each defeat, its lawyers have pledged the fight is not over. 

On Wednesday, Johnson & Johnson got its first crack at dismantling one of the verdicts in which Missouri juries have found that its baby powder caused a woman to get ovarian cancer. And a lot rides on how the U.S. Supreme Court rules in Bristol-Myers Squibb v. Superior Court of California, a closely watched case that could clarify the rules of jurisdiction for mass torts claims.