Are there LEGO sets designed for adults?
I don't think there's any LEGO set for which the age target goes any further than 16+.

Within the 16+ range, you'll find several sets, mostly in the exclusive sets (series 10xxx): mainly modular houses and some Star Wars UCS sets. Usually these are sets with a high parts count and a price to match.

There's a functionality to filter sets by age on shop.lego.com, but it doesn't seem to work properly. Neither Brickset or Bricklink appear to offer such a functionality (yet).