They can sue for copyright infringement, but since the damages are tiny, they generally don't bother. What's different since the DMCA is that "commercial scale" infringement is now a criminal offense even if you're not making any money. And if you're uploading, say by using a bittorrent client which uploads while you're "downloading", then they could make a criminal case.
Well, given the question asked, we need to be clear that the legality of downloading copyrighted content varies by country. Also, the DMCA[0] has been around for 21 years, so it's not exactly a recent change. The last time the industry went after a torrenter, it was Hunger Games (2010), IIRC; I always attributed to the Streisand affect[1].
