To my understanding of physics, there is almost no amount of thrust that would actually propel us to the speed of light, in reality. The energy costs alone would simply be too enormous.
"Folding space"/"Warping space", or shrinking the space in front of the craft while expanding the space, would seem to be the only theoretical way to achieve speeds that not only would match light speed but could surpass it and not break the laws of physics as we understand them. The drive Alcubierre proposed in the 80's, I think... maybe the 90's. I'm not sure when. A Spanish mathematician or physicist who was a fan of Star Trek.
EDIT:
My understanding of physics is pretty minimal. I'm more than happy for someone to correct me and explain what I got wrong. This type of stuff is fascinating.