to establish a colony in (a place) or extend colonial control over (an indigenous people)

Those people who were once colonized by the [English] language are now rapidly remaking it, domesticating it, becoming more and more relaxed about the way they use it — Salman Rushdie

said of plants and animals: to begin to live and breed in (a new area or environment)

often humorous to take over and occupy (e.g. a room, building, or area)