The Korean war officially commenced on June 25, 1950, Of course, it had a back history.
From 1876, the new Meiji government of Japan successfully subverted Korea's long held attachment to the Manchu ruled Qing Dynasty that had conquered China in the 17th century. In 1910 Japan occupied Korea and attempted to make it part of Japan.
Japan failed in their attempt, and as WW2 proceeded to its final end, the Japanese colonial administration handed political power to a provisional government - The People's Republic of Korea, which could be categorised as as slightly left of centre government.
In the very last days of WW2, the USSR declared war on Japan and invaded the puppet Japanese state of Manchukou (the homeland of the Manchu people, and effectively part of China since the 17th century. Within days, the very effective Soviet army was in the northern section of Korea as Japan surrendered. In Japan, the new American military occupation government, proposed to Moscow that Korea be divided into two zones. For reasons that are not entirely clear, the Russians agreed. In that way, the political entities we call North and South Korea came into existence.
The northern section of Korea had been industrialised by the Japanese, and had many left wing labour movements. There were also remnants of guerilla fighters against the Japanese. The Korean communist party emerged as the strongest political grouping. It soon subverted the People's Republic of Korea. Between 1945 and 1950 many left-wing guerilla fighters fought alongside the Chinese Communists against the Guomindang Armies of Chiang Kai Shek, After 1949, they started returning to north Korea.
The south (after 1945) became the haven for dispossessed landlords from the north and for former collaborators with the Japanese, including Koreans who had joined the Japanese Army. The People's Republic of Korea, failed in the south as the American Military occupation decided to ignore it.
Both the north and the south claimed the right to represent all Korean peoples, both built stronger armed forces and spoke of uniting Korea by force. But when war did come, with the north making a feint that turned into an invasion that swept far into the south in a matter of days.
MacArthur's very successful landing behind the North's front line changed the course of the war and the south's army and allies swept far into the North's territory. MacArthur's only mistake was to ignore the Chinese warning (the Chinese feared and American invasion of China) not to proceed to the border with China.
A stalemate resulted during the last two years of the war, but the South's supporters effectively controlled airspace and the North was effectively destroyed. Negotiations commenced and an armistice was signed on July 25, 1953, but no Peace Treaty was ever formalised between north and south Korea.
The North has often called for a formal end to the war, but no agreements ever materialised.
Now it seems that there may be a formal end to that war.