The constancy of the speed of light is one of the biggest stumbling blocks. Every observer always sees light traveling at c regardless of the speed of its source. Time dilation and length contraction are easy to confuse. As seen in a frame in which they are moving , objects are contracted and clocks tick more slowly. In their own rest frame, all lengths and clocks seem normal no matter how fast another observer sees them to move.
Some people seem to find it offensive that superluminal travel is impossible for material objects.
In the viewpoint of modern physics, the speed of light actually represents the speed at which the two long-range forces, gravity and electromagnetism, are propagated. Some relativity questions and answers are available at NASA Relativity Page For a slightly more advanced discussion, see the online lecture notes from Professor Fowler of UVa on special relativity.