SPOILER WARNING
The following contains spoilers.
Asteroid Boxes are containers found in asteroids where The Children are 'born'. At first glance they look like any ordinary cardboard box. They are beige in color and relatively small. On the back side they have symbols, similar to ones seen on the computer in the superstructure.
Mars' Box
It was seen in a cupboard in Mars' kitchen. It was placed there by Mars' parents because they wanted him to not care about it, this suggests it contains something he's not meant to see.
Claw's Box
It was found by Sepia inside the asteroid where Claw was born. Sepia was unable to open it, even though it doesn't look like it's locked. She gave it to Claw so that she could give it a try. Inside there were: