If we ever reach the technology to enable relativistic starships (basically able to accelerate at 1g or so for years at a time), then the universe is going to get seriously weird. Not only for us, but also for people in the distant future who will regularly have ancient relics from the past traveling into their time, when they will likely scarcely resemble us, and going 'Hello fellow... humans?' That'd be some next level archaeology opportunities though.
It'll also be socially odd as the elite and powerful travel off into the future seeking immortality, unable to ever return, at least so far as we currently understand.