Relativistic space travel using photonic propulsion (lasers) could accelerate a 100kg unmanned craft to 30% of the speed of light and put Mars just two days away.  Alpha Centauri, the nearest star system to our own (four light years) would be a mere 20 man-years away.  By comparison, a mission to Mars today, manned or not, takes about six months under chemical propulsion. 

Photonic propulsion however, is not without its own laws-of-physics constraints.  Using an equivalent amount of propulsive energy as currently used in a Mars rocket, and accelerating a similar sized manned craft would still require one month to reach Mars, an 83% reduction in transit time, but not quite as swift as two days... 

The technology?  Currently funded through a NASA Innovative Advanced Concepts research program [3].  Watch the video [1] or read the paper outlining the roadmap [2].

Principal Scientist: Philip Lubin (UC Santa Barbara)

References:
[1] Going Interstellar (2m video)
https://www.youtube.com/watch?v=WCDuAiA6kX0

[2] Roadmap to Interstellar Flight (PDF), Philip Lubin
http://www.deepspace.ucsb.edu/wp-content/uploads/2015/04/A-Roadmap-to-Interstellar-Flight-15-d.pdf

[3] Directed Energy Interstellar Precursors, DEEP-IN, a NASA Innovative Advanced Concepts research program
http://www.deepspace.ucsb.edu/projects/directed-energy-interstellar-precursors

[4] Reaching Mars (this article)
http://www.cnet.com/news/reaching-mars-in-a-few-days-its-possible-nasa-video-says/