In the ’60s and ’70s the United States had the necessary vision and technology to put men on the moon. They did so quickly and effectively using chemical-powered rockets. At the time, they also had grand plans for creating more powerful and efficient nuclear rockets, that would enable us to truly conquer the problems of exploring our solar system.
Unfortunately, those plans were never implemented. The cold war, economic troubles, and the public opinion of nuclear power – among other things – conspired to bury those plans.
More recently, the idea has again been raised. We have a solid foundation of research from that era to build upon; and the opportunity to create cheaper, more effective space craft using much improved technology. At the forefront of these ideas seems to be Vapor Core reactor type of nuclear engine. It is a non-polluting solution for using nuclear fuel to power our rockets between the planets.
You can also read this article, for a plain-language explanation of the technology, and how we might use it: