Can We Really Build A Space Elevator?

Are space elevators something that we could really build, or just the stuff of science fiction? 

If it is possible to actually build one, would it actually be worth it? Would it be safe? 

When it comes to the idea of space elevators there are lots and lots of questions. Some of these questions have answers, but most don't.

Check out this video to learn more about space elevators and to answer a few of the questions that come to mind.