The last one to enter commercial service was last year...but they began construction on that in 1973 before shutting down construction in the 1980's. They resumed it recently, but I don't know that this is a "modern" reactor. The last one to enter commercial service before that was over 20 years ago.
People think nuclear power (and nuclear weapons) are state of the art stuff, but in some cases, the technology is almost 50 years old. There is a reactor in New York that has been operational since Apollo 13. Granted, they have been improving...but the last time a reactor was designed and built from scratch in the US was decades ago.
We need to modernize. Nuclear power is the future.