Project Orion was supposes to reach ~10% of the speed of light by using fission bombs and could theoretically be built using 1950's technology. There are other

Project Orion was supposes to reach ~10% of the speed of light by using fission bombs and could theoretically be built using 1950's technology. There are other proposed schemes to travel at ~light speeds - light sails, nuclear fragment rockets, but I'd bet on nuclear fusion in the not so distant future. Faster than light travel may be off the table, but I see no reason why nuclear energy alone could not get us "close" to the speed of light in the next centuries or so.