How do you buff or clean concrete floors?

Question:We just moved into a loft. It has polished concrete floors which we think are really neat. However when they finished constructing the loft, construction dust has made them totally filthy. I have tried just mopping but it isn't restoring them to how they should look. I know they are polished and shiny underneath, I just don't know how to clean them. The dust has gotten into the cracks and textured parts as well. How do I buff or clean these floors and restore them to their original shine?

Answers:
Are they outside? if so, I just did this yesterday to my concrete floor I power washed it and all the dirt came out and they look great...