The US acquired several different pieces of land outside the continental US between 1867-1906. This includes:
1) Guam
2) Puerto Rico
3) Phillipines
4) Hawaii
Guam, Puerto Rico, and the Phillipines were all taken over by the US after the Spanish American War of 1898. This war saw the US helped free Cuba from Spanish control. Along with this, the Spanish agreed to relinquish control of the rest of their colonies in the Western Hemisphere.
Besides this, the US also took over Hawaii. This was done by helping Hawaiin citizens overthrow their queen and establishing a democratic system similar to the one the United States has during this time.
