As billions of people worldwide use the internet to illegally stream or download copyrighted material like music, movies and TV shows, the entertainment industry is trying to crack down on American internet service providers for complicity in the alleged crimes of their customers.

A major case before the Supreme Court on Monday could determine whether those providers can be held financially liable to the tune of hundreds of millions of dollars for “contributing” to copyright infringement if they fail to cut off internet access to any account suspected of engaging in piracy.