The Korean War, which began in 1950 and lasted until 1953, ended with an armistice agreement, not a peace treaty. This means that the two countries are still technically in a state of war.
The armistice agreement created the Korean Demilitarized Zone (DMZ), a 2.5-mile-wide strip of land that runs along the 38th parallel, which divides the Korean peninsula. The DMZ is one of the most heavily militarized borders in the world.
There have been several attempts to negotiate a peace treaty between North and South Korea, but none have been successful. The main sticking point is the issue of North Korea's nuclear weapons program. North Korea has refused to give up its nuclear weapons, and the United States and South Korea have refused to accept a nuclear-armed North Korea.
In 2019, there were some signs of progress in negotiations between North Korea and the United States, but talks broke down in 2020. Since then, there has been little progress.
The situation on the Korean peninsula remains tense, and there is always the risk that the war could start again.