The Southwestern United States (also known as the American Southwest) is the informal name for a region of the western United States. Definitions vary a great deal and have never been standardized--and many have been proposed. For example, it might include the stretch from east of Los Angeles to El Paso, and from the Mexican border to south of Denver. The population for that particular definition area is around 11 million people, with over half that in the state of Arizona. The largest metropolitan areas are Phoenix (with a population over 4 million people) and Las Vegas (about 2 million); other significant population centers in the Southwest are Albuquerque, El Paso, and Tucson. 

Most of the area was part of the Viceroyalty of New Spain in the Spanish Empire before becoming part of Mexico. European settlement was almost non-existent outside New Mexico in 1848, when it became part of the United States through the Treaty of Guadalupe Hidalgo; far southern Arizona was added in the later Gadsden Purchase. 

The geography of the region is mainly made up by four features: the Mojave, Sonoran, and Chihuahuan Deserts, and the Colorado Plateau; although there are other geographical features as well, such as a portion of the Great Basin Desert. The deserts dominate the southern and western reaches of the area, while the plateau (which is largely made up of high desert) is the main feature north of the Mogollon Rim. The two major rivers of the region are the Colorado River, running in the northern and western areas, and the Rio Grande, running in the east, north to south.
When did most of the region become part of the US?
 European settlement was almost non-existent outside New Mexico in 1848, when it became part of the United States through the Treaty of Guadalupe Hidalgo; far southern Arizona was added in the later Gadsden Purchase. 