The Oregon settlement between the United States and the United Kingdom and the Treaty of Guadalupe Hidalgo changed the map of North America by making it very nearly what it is today. These events gave large chunks of land to the United States. After these events, the US had gotten essentially all of the territory that now makes up the “Lower 48” states.
Before these events (both of which came in the 1840s) the United States was much smaller. It did not yet have the area that is now the Southwest and California. It also did not have sole possession of what became the states of Oregon, Washington, Idaho, and parts of Wyoming and Montana. The Southwest and California were part of Mexico. The US and the UK jointly owned the Oregon Country.
The Treaty of Guadalupe Hidalgo was signed after the war with Mexico. It gave the US California and the Southwest. The settlement with Great Britain split the Oregon Country, giving the area above the 49th parallel to Britain and keeping the area below that line for the US.
After the 1840s, only minor changes would be made to the boundaries of the North American countries.