In the current version of the beta, the final quest is completed when you first obtain (build) a distress beacon.
There are no further quests.
gaming.stackexchange.com/users/12944/01d55
The last (current) quest is just build the distress beacon.
Though, with the item you get from defeating the mother-ship you can build a metalwork station
so you can make/do more things.
What I did was just get some coal and explore the universe.
gaming.stackexchange.com/users/65203/Blob
Don't know if this is on time, but the UFO should be there ups in the sky.
Try jumping to see it or use a bow to hit it and see the bar, it usally sticks to a player (Now) and it's fairly easy to kill.
gaming.stackexchange.com/users/63769/Adrian
Press "E" on the Distress Beacon
gaming.stackexchange.com/users/65791/Helpful User
Yeah, no more quest so far.
Now you need to get the molten core from mothership, for me it was full of penguin like creatures with some heavy weapons.(To
defeat the mothership you need to place high stairs in the air to jump and hit the mothership).
With the molten core you build a new metalwork station and in that station you can upgrade de star map, is like a computer card.
Now you put that computer card in your conckpit and now you can go to tier 2 or B stars section, there you find new worlds with higer level threat and now you can build robots and high tech stuff, even a brain.
(I am just eploring this
so I Dont know more).
gaming.stackexchange.com/users/66312/user66312
You can make another distress beacon.
You still don't get any quests beyond this, but you DO need the item that the penguin ship drops for further building.
gaming.stackexchange.com/users/63289/Deadman
I've put distress beacon, then I haven't seen any UFO, just couple penguins, I've killed them and then there's happened nothing, no new quests etc. What should I do and/or what did I wrong? Should/can I summon UFO iteratively?
New quests don't appear
gaming.stackexchange.com
<starbound>
gaming.stackexchange.com/questions/144943
gaming.stackexchange.com/users/63230/Necronomicron
In the current version of beta, there are no further quests but you do need the item that the penguin ship drops. The UFO should be there up in the sky.  In that version of the game, there are no further quests.
The community being affirmative that there are no further quests.