This is not a lurid report, but really happened, Scientists have succeeded in creating a warp bubbleeven if only small and weak, but nevertheless detectable and existent. Just imagine, a solution to travel to the stars was just discovered and yes, really discovered, because the discovery of the warp bubble was pure coincidence, when one worked on an experiment with the Casimir effects.
What does this mean for us now? Actually nothing, it is the discovery that rocket fuel burns and has a thrust. So you can imagine it as an analogy. How much of it is needed, how much energy, how big the ship can be? All unknown, just like at the beginning of space travel when people just experimented times and there were many failures. Also this time mankind will be confronted with failures, nevertheless one will make also here progress, that I am sure. Only with the difference that we already have spaceships and create space travel into orbit without major problems^^.
Will I see the first spaceship to leave the solar system in my lifetime? I would be happy to know that mankind can also find a place outside the solar system. But I would be satisfied already if I can observe the first landing on Mars.
In Star Trek, where warp drive may have its origins, it is discovered between 2050-2063 (estimate based on the age of the developer) and has advanced humanity since then. Maybe we will get ahead of the fictitious date and thus fly with warp drive before 2063. But well, one can dream, Captain Picard... You have the bridge
Further sources:
English 
German 
French 
Czech