This is a complicated speculative question, but there are some interesting things to consider:
1. Special relativity dictates that one cannot travel AT the speed of light. However, it does not really say much of value at tachyonic speeds (beyond the speed of light) because the computed quantities are imaginary then. Approaching the speed of light from below would require an infinite amount of energy.
2. By the General Theory of Relativity, there are regions of space where the laws of physics break down (inside a black hole for example).
3. There are even more speculative constructs called wormholes which might connect distant regions of space.
4. There have been some demonstrations of quantum teleportation in the laboratory for very small quantities of material. It is not clear if this will lead to any practical technologies ever, but if it does, it might take centuries.
5. Probably the special and general theories of relativity are incomplete at best, and possibly even inaccurate. For example, we seem to be observing some sort of evidence of antigravitational forces on cosmic scales, which contradict our standard relativistic gravity theory. No one knows what any of this means yet, if anything.
6. Quantum mechanics is very complicated, and we probably only are scratching the surface of quantum mechanics. Attempts to connect quantum mechanics with gravity have so far been fairly disappointing. There is clearly a lot more physics that we do not understand at all, and when more is uncovered, it is not clear what sorts of technology will be possible.