With your examples, the more we understood science the more likely it was to accomplish them.
With interstellar travel, the more we understand the science the LESS LIKELY it seems possible.
The speed of light is not an engineering limitation, like the speed of sound is. The speed of light is actually two things: 1) the speed at which massless particles in the absence of external matter and fields travel and 2) a constant defining the interrelationship between time and space.
Mathematically, because of (2) the speed of light appears the same to all observers no matter how quickly or slowly they themselves are moving with respect to the source of light.
The geometric way of looking at this is as follows: We believe that we are free to move in all three dimensions of space at any speed we desire. However, the truth is that the dimensions of space and time are actually connected, and for particles which have mass, it is impossible to move through space without also moving through time. In fact, because of (2) we are actually confined to a much smaller subset of space-time. Space and time are potentially "infinite" but some regions of space-time are not actually accessible to us. They lie outside of what is called our "light cone." Objects traveling faster than the speed of light would actually be moving through this geometrically inaccessible region.
When people talk about tesseracts, Einstein-Rosen bridges, and "warp-drives" they are talking about mathematically possibilities, which -- if they existed physically -- would also imply time travel. If you moved outside of the light cone of our thread of history, to travel faster than the speed of light, you would necessarily intersect the light cones of different eras of the universe as you moved. When you stopped, you would no longer be in our light cone, but in another one. Time travel.