If we survive the next two centuries as an advanced civilization (odds are we won't), then I believe we can continue learning and will eventually figure out faster than light (FTL) travel.

That being said, I don't believe we will investigate the universe personally. Our bodies are part of this planet. Literally. Existing in space for any length of time is very unhealthy for us. By the time we get FTL, AI and robotics technology will be advanced enough that sending near sentient avatars of ourselves would be the only logical choice.

Not needing life support on the rockets makes exploration so much easier and cheaper. Look at what NASA is doing on Mars now as a perfect example.

Not just BTW: It is my belief that if aliens have visited earth, it is in the same way as I listed above, as the aliens would be a part of their home planet the same way we are.