The last two states to join the United States were Alaska, in January 1959, and Hawaii, in August 1959. Prior to Hawaii and Alaska, the most recently added states were New Mexico, in January 1912, and Arizona, in February 1912. In many cases, areas that later became states were annexed by the United States years earlier but not granted statehood.
Statehood is granted by the U.S. Congress, but the process of state formation is not entirely defined within the U.S. Constitution. Historically, a territory of the United States has held a referendum vote, and if the majority of voters supported statehood, the territory petitioned Congress. The territory is required to adopt a constitution in line with the U.S. Constitution, and statehood is voted on by Congress and approved by the President.
While no valid petition for statehood has ever been rejected, some of the most recent states have delayed becoming states. Alaska delayed statehood for 92 years, while New Mexico's first effort at statehood was rejected due to political infighting, delaying the state's inclusion for nearly 40 years. Oklahoma was the 46th territory to become a state, despite being a U.S. Territory for over 100 years before becoming a state in 1907.