These films typically feature stories and characters with moral vagueness, paranoia, and/or vengeance. In terms of production, they often employ Dutch angles, unbalanced framing, and lots of shadows and dark coloration. As for the marketing, neo-noirs are usually aimed at adults, who tend to prefer the darkness and mystery, as opposed to kids/teens and their blockbuster action films.
One example of a neo-noir would be Watchmen, a grim R-rated 2009 comic book film directed by Zack Snyder. This production tells a story revolving around a paranoid detective and vigilante that investigates a murder mystery, as his former superhero allies are seemingly targeted by a criminal. As you can tell from that sentence alone, this film employs practically all the aforementioned elements of a neo-noir film. Without giving too much away, the film follows a dark twist and goes on to explore a great moral dilemma that would likely leave the viewer psychologically thrilled. Most of the movie takes place in the dark, too.
Frank Miller's Sin City is an almost iconic film of the neo-noir sub-genre.
Seven, stylized as Se7en, is an intense, mind-blowing psychological thriller and absolute neo-noir.
Straight out of South Korea, Oldboy is indeed kinda old but still fresh enough to be considered neo-noir.
Finally, Looper by Rian Johnson is widely considered to be one of the best neo-noirs out there.