Psychological thrillers are action-packed dramas that often focus on the unstable mental state of their characters. There's significant crossover with the mystery, slasher, and horror anime genres. Because the content is often pretty disturbing, this anime is often geared towards adults. While most people think of live-action films like Fight Club or Silence of the Lambs when they think about psychological thrillers, there's also some pretty good thriller anime out there too.
There's a lot of psychological thriller anime that's not bad. Not great, but not bad. Some shows deal in harmful stereotypes, others lack good character development, and some have art that's just kind of weird and hard to look at. But, despite the imperfect nature of the genre, you'll definitely be able to find some decent psychological thriller anime series that you won't regret watching.