Detected by the radial velocity method, measuring the parent star being pulled toward and away from us by a variation of at little as 2-3 meters per second! It always blows my mind that we can measure that.
I know, right? It's mindblowing that we can pass that light through a spectrograph and get the radial velocity just by the infinitesimal doppler shifts. Read about HARPS and the followup projects for more.
I don't understand anything about it, but I think I read that LIGO has been enhanced with a technique involving "squeezed light" which allows some bypassing of heretofore assumed fundamental physical limits through quantum wizardry.
Something else I read about, that doesn't sound like it involves far out voodoo tech to me, that I wish I'd live long enough to see, is putting a probe out far enough and in the right position, to use the Sun's gravity as a telescope lens.
...and (maybe) actually get pictures of extrasolar planets.
I don't know if those pictures would be like Hubble's view of Pluto, or in principle could be much better.
If I could have one wish for something extraterrestrial, that is more achievable, it would be close up pictures of Haumea. Eris and others too, but Haumea most of all.
I care nothing at all for Mars colonies, but the most exciting thing about Starship for me is the hope that maybe combining it with in-orbit refueling could enable quicker travel to the outer solar system and loitering/orbiting instead of flying by at top speed.
There's a funny paradox-like situation that arises in space flight where because of the distances involved/ time taken, it might be better to wait some time for a faster method of flight to develop. Of course, it is up for debate whether there are many more ways of propulsion that are yet to be invented.