By the end of the 21st century, thousands of asteroids have been colonized. Most colonized astroids follow a similar model; hollow out a cylindrical shape in the center of an asteroid, use the hollowed material to construct a cylinder, and spin it up for artificial gravity. This process leaves surplus rock and ore from the hollowing out process, which is typically refined and either sold or turned into spacecraft. The structures of the colony itself are built within this cylinder, with the outer levels having the most gravity. The rock of the asteroid itself (which does not spin) offers protection from meteors and harmful solar radiation, and the docking ports are built into this non-rotating section, connected to the spinning cylinder at the center.
Every asteroid colony has its own unique flavor, quirks, and oddities. The belt is the wild west of space, and every colony is a new frontier town with its own mayor, sheriff, and townspeople. Kicking around the asteroid belt can be a source of endless variety for a campaign, not to mention danger.