TL;DR
Humanity may launch its first spacecraft aimed at another star before the decade ends. A nonprofit called Fermi Explorer plans a $15 million, donor-funded probe toward the star system Alpha Centauri by the end of 2029. It is a slow, symbolic trip: about 80,000 years to get 99% of the way, with radio contact lost after a year. Everything faster lives on paper. The best-known plan to reach the stars within a lifetime, Breakthrough Starshot's laser-pushed sail, is paused until lasers get a hundred to a thousand times cheaper. Warp drives are real mathematics but have no workable design. For now the stars are a matter of intent and arithmetic, and the arithmetic says the hard part is energy.
Below the line, for paid subscribers: The full story: where it stands, how we got here and what's dated next; our Odds board on 5 milestones, starting with "The warp-bubble deflector-shield preprint is published after peer review by 2027"; and every source.