Nuclear rockets are nothing new but the reason they have not seen significant use is because first you have to launch them to orbit. Rockets have a not-insignificant chance of exploding or crashing during launch and when you have them loaded with lots of fissionable material the effect is like a dirty bomb that has a good chance of scattering highly toxic, radioactive debris over a large area.
I suspect we will not see nuclear rockets until we develop a fusion-based one because, unlike fission-based designs fusion uses light, non-toxic, stable isotopes as fuel and so is likely to be no more dangerous than current chemical rockets.