The most promising proposal that I have heard is orbiting thin film mirrors, manufactured in place by robotic machines, which focus more sun to thaw the frozen water that exists in the Marian soil — the water would then boil in the low pressure and enter the atmosphere. The material for the mirrors could be obtained from asteroids, avoiding the need to overcome gravity wells. The atmosphere does not have to be Earth sea level pressure. I believe that humans can survive at the “Armstrong limit” (7% of sea level pressure), as long as they have a breathing mask.

Of course, it is a huge undertaking. There would have to be something to gain — but perhaps an entire newly habitable planet is an incentive?