TL;DR
A rocket that comes back whole and flies again within days could make getting to space cheap enough to matter, and SpaceX may try the hardest piece in November. The upper half of its giant Starship rocket, the part that actually reaches space, just passed its last full-power engine test before Flight 15, when SpaceX plans to try catching it in the arms of the launch tower for the first time. SpaceX has caught the lower half three times; it has never caught the ship. If it works, both halves of an orbital rocket would come back for the first time, by Musk's account, and the turnaround between flights could shrink from months to days. That is the pace SpaceX would need for its claimed weekly launches in 2027 and for the string of refueling flights a Moon landing requires.
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 6 milestones, starting with "SpaceX catches a Starship upper stage with the launch tower by 2026"; our labeled speculation on what it adds up to; and every source.