In classical Greece the fundamental social unit was the polis, often mistakenly referred to as city-states. Unlike modern Greece, ancient Greece was not a unitary nation-state, but consisted of independent communities. These communities or poleis had typically a very limited territory as well a population of only a few thousand inhabitants.
Given that ancient Greece was relatively infertile and hence a difficult place for agriculture, overpopulation was a great issue for any Greek polis. Their solution was, however, quite simple. Once the population of a population was too large to sustain, a part of the citizens had to leave the polis and to settle elsewhere.
The would-be emigrants where either volunteers or assigned by lottery. The polis would give them the necessary supplies to survive their journey and to set up a new settlement. Such new settlement was called a colony and was a polis in its own right.
Unlike modern colonies ancient Greek colonies were independent and self-governing communities. Nevertheless colonies did maintain close cultural and economic ties with their mother-city or metropolis. And once the colony had become too large, the whole cycle was repeated again. This way Greek civilization was spread across the Mediterranean.
Earlier we have discussed the similarities between small space settlements (such like Bernal spheres or toroidal settlements) and Greek poleis. It is not unlikely that future space settlements, in particular those in the Main Asteroid Belt, might follow a similar pattern of colonization.
Greek colonies on Wikipedia