The majority of roach species live outdoors in warm, wet, tropical environments, according to insect expert Debbie Hadley. BugGuide adds that most native North American roaches are woodland insects; the two most-common pest roaches, the German cockroach and the American cockroach, are invasive species.
Both German and American roaches are found worldwide, as noted by Animal Diversity Web. Neither species is from the location suggested by its name. German roaches are native to Southeast Asia, while American roaches are native to Africa.
German roaches, as described by Animal Diversity Web, live in a large range of climates and are the most common household pest roach around the world. American roaches prefer to live in commercial buildings that store or prepare food and in sewers. It is less common to find them in residences.