Researchers from Harvard have shown that thin layers of silica aerogel could warm the surface of Mars and block UV radiation while still letting visible light through. That could be enough to keep water liquid and let plants photosynthesize within a given region.
Could we one day terraform Mars? According to a new NASA study, don't hold your breath. By the most generous estimate, there isn't enough material on the Red Planet to even begin to provide it with a minimal atmosphere – much less make it suitable for colonization.