It all has to do with Einstein's Theory of Relativity -- apparently since time and space are kinda the same thing, it is true that both are subjective. For example, we're stuck on the Earth, trapped by its gravitational field, so we perceive the flow of time in the context of an Earth-sized rocky mass.
But as Einstein calcu-malated, as you accelerate, approaching the speed the light, time ( for you at least) slows down. If you traveled through the solar system at say, 670 000 000 mph, you would perceive that 12 months had passed, but when your returned to Earth you'd find that 10 years had passed. So in theory travelling forward in time is not only possible, it's also kinda how the GPS in your car works. Going back through time to make sure your parents meet in high school though, that we haven't quite got to yet, and some would say the fact that no one has yet come back and said they were from the future is pretty much proof of that...well except for that one guy...
The Future: Government-issued track suits mandatory when watching caveman soccer on laser disc.
The trick is entanglement, an atomic particle can change its location in space without travelling the distance between point A and point B. It's called "Spooky action at a distance" and again, we've actually done it, albeit on the tiniest scale. What comes next is figuring out how to multiply the effect for a jumble of particles like you and me, successfully zapping you out of a tight spot and back to the safety of the Enterprise.
Just make sure there aren't any damn bugs in the thing when you zap through.
The Ion Engine
In practical application, it functions on exponential acceleration as opposed to traditional chemical combustion rockets that blast their way free of Earth's gravity then rely on inertia from that blast to reach their destination.
You're making the noises in your head right now.
A spacecraft carrying an Ion engine doesn't need to use the gravity of other solar bodies to slingshot around to its next target. It has the acceleration and fuel economy to reach its destination under its own power without borrowing inertia from planets.
The "Dawn" spacecraft was NASA's first Ion Engine-propelled spacecraft which after flybys of Mars, headed to the Asteroid Belt.
The Quantum Computer
This one I still have trouble grasping but in essence, we're talking about a computer capable of bajillions of computations per second made possible by some of the same theories behind the teleportation idea.
Quantum Computation will become a major tool in the next decades as we get closer to replicating the power of the human brain and come up with artificial intelligence than can pass the Turing Test (that is, a computer that seems indistinguishable from a human in a blind interaction like a skype conversation.)
The Singularity is near...
We may one day soon have a Douglas Adams, Hitchhikers-Guide to the Galaxy-esque supercomputer that can tell us the meaning of life! Spoiler alert, the answer is 42.
Imagine thousands of robots the size of red blood cells floating around your circulatory system. I hate the feeling of ants crawling all over me so I can imagine some might find an invasion of Insecticons under your skin a little unnerving. But if you can get past the squeamishness of the idea, these little buggers potentially could team up with your anti-bodies to wipe out incoming threats and super charge your immune system.
To hell with beta-blockers, you could have an army of Robocops patrolling for viruses and other undesirables in your body. One might not be able to say your body is a temple, but a fortress, hellz yeah!
So we have much to look forward to in the magical world of science, so long as nothing gets blown to bits before the end of 2012. Certainly, many ethical and legal hurdles surround future developments. We can only strive for positive leadership in these fields to guide us into a technological utopia (I nominate Google) -- and ward off the darker side of our nature....
Because as the engineers at Cyber-Dyne will tell you, the sleep of quantum computation produces skyNET.