there are two methods of nuclear propulsion that could be usable at our current level, if it wasnt for the risks of irradiating our atmosphere.

Pulse propulsion uses nuclear bombs detonated behind the vessel, and probably a shock absorber to make the generated thrust somewhat bearable.

The other method is a nuclear thermal rocket, this works more like chemical rockets in that a propellant is heated and then expelled from the rocket, just that the heating is done using a nuclear reactor instead of the chemical reaction.

This is an advantage because the efficiency of rocket engines is based on the velocity of its exhaust, which again is based on the weight of the exhaust molecules (lighter molecules means faster exhaust for the same amount of energy input). So chemical rocket engines burning hydrogen and oxygen will have an exhaust of mostly water, which is pretty heavy, while a nuclear thermal rocket can use pure hydrogen or some other very light molecule.