Science of Time Travel

A staple of science fiction is time travel. Despite how overly complex the concept can get, many stories have written about. So, is time travel actually possible?  Just a disclaimer, I am not a physicist. As such, I am using other sources for this information (see below).

Theoretically, you can actually time travel by going fast enough. As you get closer to the speed of light, time slows down for you (and just you). However, you do not notice this effect until you stop. From your perspective, you could travel a month and find yourself years into the future (NASA).
However, there are several problems with time travel. A time machine would need fuel comparable to the power of the star. (Kaku) Going at such speed would kill any human that attempts it. (The Week) Also if by some miracle you manage to build a machine that somehow bypassed these problems, there is no way back leaving thus trapping you in the future (NASA). So even though in theory it is possible, it is unlikely you'll be visiting ancient Rome anytime soon.

Some people have proposed a work around. Based on Einstein's theories of relativity, it has been theorized wormholes could be the solution. Wormholes, for those not in the know, have the ability to connect two different points of space and time. (Kaku)
However, this has problems too. No wormhole has ever been discovered. As of the time writing, they only exist in the realm of theory. (The Week) According to current theories, wormholes would be 10^–33 centimeters large. (Redd) As such, wormholes don't seem particularly practical either.
References:
http://spaceplace.nasa.gov/review/dr-marc-space/time-travel.html
http://mkaku.org/home/articles/the-physics-of-time-travel/
http://www.theweek.co.uk/health-science/59106/time-travel-four-ways-in-which-it-could-be-possible
http://www.space.com/20881-wormholes.html